hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Polynomial method in combinatorics
In mathematics, the polynomial method is an algebraic approach to combinatorics problems that involves capturing some combinatorial structure using polynomials and proceeding to argue about their algebraic properties. Recently (around 2016), the polynomial method has led to the development of remarkably simple solutions to several long-standing open problems.  The polynomial method encompasses a wide range of specific techniques for using polynomials and ideas from areas such as algebraic geometry to solve combinatorics problems.  While a few techniques that follow the framework of the polynomial method, such as Alon's Combinatorial Nullstellensatz, have been known since the 1990s, it was not until around 2010 that a broader framework for the polynomial method has been developed.

Restricted sumset
In additive number theory and combinatorics, a restricted sumset has the form

where  are finite nonempty subsets of a field F and  is a polynomial over F.

If  is a constant non-zero function, for example  for any , then  is the usual sumset  which is denoted by  if

When

S is written as  which is denoted by  if

Note that |S| > 0 if and only if there exist  with
Elizabeth Aston
Elizabeth Edmondson (21 February 1948 – 11 January 2016), also known under the names Elizabeth Aston and Elizabeth Pewsey, was an English author who wrote primarily in the mystery, historical, and contemporary fiction genres. She studied Jane Austen while a student at St Hilda's College, Oxford, and many of her published stories were adaptations and sequels of Austen's works, beginning with Mr. Darcy's Daughters in 2003. Edmondson also founded a youth holiday orchestra to provide musical opportunities for local young people in the York area, an organisation that has operated since 1992. Her son, Anselm Audley, is a fantasy author.

Mr. Darcy's Daughters
Mr. Darcy's Daughters is a 2003 novel by the English author Elizabeth Aston, published by Simon & Schuster in the United States. Set in 1818, Mr. Darcy's Daughters is written as a sequel to Jane Austen's 1813 novel Pride and Prejudice. It features the five daughters of Fitzwilliam Darcy and Elizabeth Bennet – aged 21 to 16 – as they navigate London society in the absence of their parents, who have embarked on a diplomatic post to Constantinople. In London, the sisters meet new friends and find themselves in various romantic entanglements, all while learning what is acceptable behaviour among the city's elite.
2009–10 Ohio State Buckeyes men's basketball team
The 2009–10 Ohio State Buckeyes men's basketball team represented Ohio State University in the 2009–10 college basketball season. Their head coach was Thad Matta, in his 6th season with the Buckeyes. The team played its home games at Value City Arena in Columbus, Ohio, and is a member of the Big Ten Conference.

On March 14, 2010, the Ohio State Buckeyes won the Big Ten tournament for the first time since 2007, defeating the Minnesota Golden Gophers 90–61.  The Buckeyes now have three Big Ten tournament Championships (2002, 2007, 2010), the most of any team in the Big Ten.  The Buckeyes also made the 2010 NCAA Division I men's basketball tournament, making it for the second consecutive year and four out of the six years Thad Matta has been head coach. They were a 2 seed in the Midwest Region. Ohio State ended the 2009–10 season with a loss to 6 seed and AP #15 Tennessee Volunteers in the Sweet Sixteen. Their final record was 29–8.

2009–10 Tennessee Volunteers basketball team
The 2009–10 Tennessee Volunteers basketball team represented the University of Tennessee in the 2009-10 NCAA Division I men's basketball season. This was the fifth season for Bruce Pearl as the Volunteers' head coach. The team, a member of the Eastern Division of the Southeastern Conference, played its home games at Thompson-Boling Arena. They finished the season 28–9, 11–5 in SEC play and advanced to the semifinals of the 2010 SEC men's basketball tournament before losing to Kentucky. They received an at-large bid to the 2010 NCAA Division I men's basketball tournament, earning a 6 seed in the Midwest Region. They defeated 11 seed San Diego State in the first round and 14 seed Ohio to advance to the Sweet Sixteen. In the regional semifinal they defeated 2 seed and AP #5 Ohio State to advance to the first Elite Eight in school history. They were defeated by 5 seed and AP #13 Michigan State in the regional final to end their season.
Juan Huerta Montero
Juan Huerta Montero (21 February 1964 – 3 September 2010) was a Mexican politician from the National Action Party (PAN). From 2009 to 2010 he sat in the Chamber of Deputies 
to represent Guanajuato's 1st district during the 61st session of Congress.

On 3 September 2010, Huerta and a fellow deputy, Guillermo Zavaleta Rojas, died in a plane crash near Bahías de Huatulco International Airport in Oaxaca.
He was replaced for the remainder of his congressional term by his alternate, Aránzazu Quintana Padilla.

Guillermo Zavaleta Rojas
Guillermo José Zavaleta Rojas (19 March 1976 – 3 September 2010) was a Mexican politician from the National Action Party. From 2009 to 2010 he served as Deputy of the LXI Legislature of the Mexican Congress, representing Guanajuato.

On 3 September 2010, Zavaleta and a fellow Deputy, Juan Huerta Montero, died in a plane crash near the Bahías de Huatulco International Airport.
Silsiilay
Silsiilay (English: Stories) is a 2005 Indian Hindi-language romance film written and directed by Khalid Mohammed. The film stars Tabu, Bhumika Chawla, Riya Sen, Celina Jaitly, Anita Hassanandani, Divya Dutta, Rahul Bose, Jimmy Sheirgill, Ashmit Patel and Kay Kay Menon, with Shah Rukh Khan in a special appearance. It was released on 17 June 2005.

Kay Kay Menon
Krishna Kumar Menon (born 2 October 1966), known professionally as Kay Kay Menon, is an Indian actor who works predominantly in Hindi cinema, and occasionally in Gujarati, Tamil, Marathi and Telugu films. He is best known for his roles in films such as Black Friday (2004), Deewar (2004), Sarkar (2005), Shaurya (2008), Gulaal (2009), Haider (2014), Baby (2015). He has starred in web series such as Special Ops, Farzi, The Railway Men and Citadel: Honey Bunny.
Barry Mungar
Barry Mungar (born November 4, 1961) is a Canadian former professional basketball player. Following his college career at St. Bonaventure, he went on to play professionally in Europe. He was a key member of the Canadian national team in the late 80's, appearing with the team in several major tournaments, including the 1988 Summer Olympics in Seoul.

Canada men's national basketball team
The Canada men's national basketball team (French: Équipe du Canada de basketball masculin) represents Canada in international basketball competitions since 1923. They are overseen by Canada Basketball, the governing body for basketball in Canada.

In 10 Olympic appearances, Canada has won one medal in basketball – a silver at the 1936 Games in Berlin. The team finished fourth in 1976 and 1984. Canada has won six medals at the FIBA AmeriCup – two silver medals in 1980 and 1999, as well as four bronze medals in 1984, 1988, 2001, and 2015. In recent decades, the team also won its first medals at the Pan American Games, a silver medal in 2015, and the FIBA World Cup, a bronze medal in 2023.

The Canadian senior national team won its only gold medal at a university-level tournament, the 1983 Summer Universiade, which the country hosted in Edmonton, Alberta.
Nicolás Pereda
Nicolás Pereda (born 1982) is a Mexican-Canadian film director. His films regularly blend aspects and techniques of both narrative fiction and documentary filmmaking. His films include Where Are Their Stories? (2007), Summer of Goliath (2010), Tales of Two Who Dreamt (2016), Fauna (2020), Lázaro at Night (2024), and Copper (2025).

Summer of Goliath
Summer of Goliath (Spanish: Verano de Goliat) is a 2010 Canadian-Mexican-Dutch drama film written and directed by Nicolás Pereda.

A hybrid between fiction and documentary, the film won the Orizzonti competition at the 67th edition of the Venice Film Festival.
Photoheterotroph
Photoheterotrophs (Gk: photo = light, hetero = (an)other, troph = nourishment) are heterotrophic phototrophs—that is, they are organisms that use light for energy, but cannot use carbon dioxide as their sole carbon source. Consequently, they use organic compounds from the environment to satisfy their carbon requirements; these compounds include carbohydrates, fatty acids, and alcohols. Examples of photoheterotrophic organisms include purple non-sulfur bacteria, green non-sulfur bacteria, and heliobacteria. These microorganisms are ubiquitous in aquatic habitats, occupy unique niche-spaces, and contribute to global biogeochemical cycling. Recent research has also indicated that the oriental hornet and some aphids may be able to use light to supplement their energy supply. Some recent research has even found hints of photoheterotrophy in a few eukaryotes, though it's still being studied.

Heliobacteria
Heliobacteria are a unique subset of bacteria that process light for energy. Distinguishable from other phototrophic bacteria, they utilize a unique photosynthetic pigment, bacteriochlorophyll g and are the only known Gram-positive phototroph.  They are a key player in symbiotic nitrogen fixation alongside plants, and use a type I reaction center like green-sulfur bacteria.

RNA trees place the heliobacteria among the Bacillota. They have no outer membrane and like certain other Bacillota (Clostridia), they form heat-resistant endospores, which contain high levels of calcium and dipicolinic acid. Heliobacteria are the only Bacillota known to be phototrophic.
Mary Eunice McCarthy
Mary Eunice McCarthy (March 4, 1899 – August 7, 1969) was an American screenwriter, playwright, journalist and author, perhaps best known today as the screenwriter of, and driving force behind, the biopic Sister Kenny (1946).

Sister Kenny
Sister Kenny is a 1946 American biographical film about Sister Elizabeth Kenny, an Australian bush nurse, who fought to help people who suffered from polio, despite opposition from the medical establishment. The film stars Rosalind Russell, Alexander Knox, and Philip Merivale.

The film was adapted by Alexander Knox, Mary McCarthy, Milton Gunzburg (uncredited), and Dudley Nichols from the book And They Shall Walk, by Elizabeth Kenny and Martha Ostenso, and directed by Dudley Nichols.
Đa Kao
Đa Kao is an area in the southside of Tân Định ward, it plays a role as administrative centre also a part of the city historic central business district along with some nearby ward. It was a ward (phường) of District 1 in Ho Chi Minh City, Vietnam, but was dissolved following Vietnam's 2025 administrative reforms since July 2025.

Tân Định, Ho Chi Minh City
Tân Định (Vietnamese: Phường Tân Định) is a ward of Ho Chi Minh City, Vietnam. It is one of the 168 new wards, communes and special zones of the city following the reorganization in 2025.

On June 16, 2025, the Standing Committee of the National Assembly issued Resolution No. 1685/NQ-UBTVQH15 on the arrangement of commune-level administrative units of Ho Chi Minh City in 2025 (effective from June 16, 2025). Accordingly, the entire area and population of Tân Định ward, along with part of the natural area and population size of Đa Kao ward after the rearrangement under Clause 1, Article 1, are reorganized to form a new ward named Tân Định.
Phil Smyth
Philip John Smyth AM (born 11 May 1958) is an Australian former professional basketball player and coach. He won three National Basketball League (NBL) championships with the Canberra Cannons before going on to be a three-time championship-winning head coach of the NBL's Adelaide 36ers. Smyth was a four-time Olympian with the Australian national basketball team.

Canberra Cannons
The Canberra Cannons were a professional men's basketball team that competed in Australia's National Basketball League (NBL). They went into financial administration in 2003 and were relocated to Newcastle, where they became the Hunter Pirates. After this venture also folded the team was relocated to Singapore and played as the Singapore Slingers for the 2006–07 season.

The Cannons were runners-up in the inaugural 1979 competition and then won three championships in 1983, 1984 and 1988. They were also runners-up in 1989.
Yuka Murofushi
Yuka Murofushi (室伏 由佳, Murofushi Yuka; born 11 February 1977) is a retired Japanese discus and hammer thrower.

Murofushi comes from a hammer throwing family, as her father Shigenobu Murofushi is a former Olympian and held the Japanese record for decades, and her brother Koji Murofushi, is the 2004 Olympic champion in the event. Her mother, Serafina Moritz, is Romanian, and former European junior javelin champion and senior champion for Romania. Her parents are now divorced.

She won the 2010 Japanese title in both the discus and hammer throw events.

Koji Murofushi
Alexander Koji Murofushi (室伏 アレクサンダー広治, Murofushi Arekusandā Kōji; born 8 October 1974) is a Japanese former hammer thrower and sports scientist. He has been among the world elite since the 2001 World Championships, where he won the silver medal. He was the 2004 Olympic champion. In 2011, he was crowned world champion.
Étienne Gaboury
Étienne-Joseph Gaboury CM OM (April 24, 1930 – October 14, 2022) was a Canadian architect from Winnipeg, Manitoba.  He was noted for designing key buildings in his hometown, such as the Royal Canadian Mint building, Esplanade Riel, Saint Boniface Cathedral, and the Precious Blood Church, and was regarded as the province's greatest architect.

Precious Blood Roman Catholic Church (Winnipeg)
The Precious Blood Roman Catholic Church (French: Église du Précieux Sang) is a Roman Catholic parish located in the St. Boniface neighbourhood of Winnipeg, Canada. The church was designed by Canadian architect Étienne Gaboury.  Construction of the building was completed in 1968. The church's tipi-inspired shape has been called Gaboury's most recognizable work by the Winnipeg Architecture Foundation.
Stars Academy season 1
Stars Academy is a Hong Kong singing competition television series to find young singing talents. The first season premiered on 10 April 2021 and continued until 19 July 2021 for 14 episodes. Hosted by Sammy Leung, the show featured Hacken Lee as the coaching supervisor, along with AGA, Pakho Chau, Vincy Chan, JW, Gin Lee, and Janice Vidal as coaches. Throughout the competition, several performances gained popularity among the viewers, including Chantel Yiu's "Love Prediction" (戀愛預告), Gigi Yim's "Without You, I Still Love You" (沒有你還是愛你), and Yumi Chung's "Wild City" (狂野之城). The show was won by Gigi Yim. Following the finale, the contestants held a 4-day live concert titled First Live on Stage from 12 to 15 August 2021. The programme's popularity led TVB to continue its run for a second season (2022). It also inspired other TV shows, including the musical television series Forever Young at Heart (2021—2022) and the youth talent singing show Stars Junior Academy (2022).

Stars Academy season 2
Stars Academy is a Hong Kong singing competition television series to find young singing talents. The second season, also known as Stars Academy 2, premiered on 11 June 2022 and concluded on 2 October 2022, spanning 15 episodes. The competition followed a similar structure to the previous season, with individual and group performances and eliminations based on scores. Eric Kwok and Hanjin Tan served as coaching supervisors, alongside a team of coaches consisting of Vincy Chan, JW, Eman Lam, Phil Lam, Gin Lee, and Alan Po. Jasmine Yam was announced as the winner on 2 October 2022.  Throughout the competition, Yam gained notable popularity, securing the top position on the audience popularity list for nine weeks. A post-competition live concert titled Prom Night was held on 1 November 2022 featured performances by most contestants, with a special appearance by Eric Kwok.
Pterygopalatine ganglion
The pterygopalatine ganglion (aka Meckel's ganglion, nasal ganglion, or sphenopalatine ganglion) is a parasympathetic ganglion in the pterygopalatine fossa. It is one of four parasympathetic ganglia of the head and neck, (the others being the submandibular, otic, and ciliary ganglion).

It is innervated by the Vidian nerve (formed by the greater superficial petrosal nerve branch of the facial nerve and deep petrosal nerve) and maxillary division of the trigeminal nerve. Its postsynaptic axons project to the lacrimal glands and nasal mucosa.

The flow of blood to the nasal mucosa, in particular the venous plexus of the conchae, is regulated by the pterygopalatine ganglion and heats or cools the air in the nose.

Submandibular ganglion
The submandibular ganglion (or submaxillary ganglion in older texts) is part of the human autonomic nervous system. It is one of four parasympathetic ganglia of the head and neck. (The others are the otic ganglion, pterygopalatine ganglion, and ciliary ganglion).
Srbuk
Srbuhi Sargsyan (Armenian: Սրբուհի Սարգսյան IPA: [sərpʰuhˈi sarkʰsjˈan]; born 3 April 1994), professionally known as Srbuk (Armenian: Սրբուկ), is an Armenian singer. She first came to prominence after competing in season one of the Armenian version of The X Factor, where she placed as the runner-up. In 2018, she competed in season eight of The Voice of Ukraine, placing fourth. Srbuk represented Armenia in the Eurovision Song Contest 2019 in Tel Aviv, Israel, with the song "Walking Out".

Walking Out (song)
"Walking Out" is a 2019 song by Armenian singer Srbuk. It represented Armenia at the Eurovision Song Contest 2019 in Tel Aviv, Israel after being internally selected by the Public Television Company of Armenia (AMPTV), Armenia's broadcaster for the Eurovision Song Contest. Composed by Lost Capital and tokionine, the lyrics of the song were written by Garik Papoyan, who had previously co-written Armenia's 2014 entry for Aram Mp3. It did not advance to the final.
France Nuyen
France Nuyen (born France Nguyễn Vân Nga on 31 July 1939) is a French-American actress, model, and psychological counselor. She is known to film audiences for playing romantic leads in South Pacific (1958), Satan Never Sleeps (1962), and A Girl Named Tamiko (also 1962), and for playing Ying-Ying St. Clair in The Joy Luck Club (1993). She also originated the title role in the Broadway play The World of Suzie Wong, based on the novel of the same name. She is a Theatre World Award winner and Golden Globe Award nominee.

A Girl Named Tamiko
A Girl Named Tamiko is a 1962 American romantic drama film directed by John Sturges and starring Laurence Harvey and France Nuyen, with Martha Hyer, Gary Merrill, Michael Wilding, and Miyoshi Umeki. It is based on the 1959 novel of the same title by Ronald Kirkbride.

It was filmed on location in Japan in Technicolor and Panavision, and released by Paramount Pictures.
Dumb Things
"Dumb Things" or "I've Done all the Dumb Things" is a song by Australian rock group Paul Kelly and the Coloured Girls, released as the fourth single from their second album, Under the Sun. It was released by Mushroom Records imprint White Label Records in January 1989 and reached No. 36 on the Australian Recording Industry Association (ARIA) Singles Chart. In the US, it was released under the band name, Paul Kelly and the Messengers, which reached No. 16 on the Billboard Modern Rock chart. A music video, directed by Larry Williams, was provided for the single – a still from the clip is used as the single's cover.

Under the Sun (Paul Kelly album)
Under the Sun is the second album by Australian rock group Paul Kelly & The Coloured Girls and was originally released in December 1987 by Mushroom Records. In the North American and European markets, it was released by A&M Records in 1988 with the band credited as Paul Kelly & The Messengers, with a different track order and listing.

On the Australian albums charts, it peaked at #19, with the single "To Her Door" peaking at #14. Another single, "Dumb Things," peaked at #36 in early 1989 on the Australian Recording Industry Association (ARIA) singles charts; it reached #16 on the Billboard Modern Rock chart. The song was included in the soundtrack for the 1988  Yahoo Serious film Young Einstein.

"To Her Door" won an ARIA Award in 1988 for 'Best Video' directed by Claudia Castle. In 2001, the Australasian Performing Right Association (APRA) listed the Top 30 Australian songs of all time, including "To Her Door," written by Kelly.
King Kuang of Zhou
King Kuang of Zhou (Chinese: 周匡王; pinyin: Zhōu Kuāng Wáng), personal name Ji Ban, was a king of China's Zhou dynasty.

King Kuang's father was King Qing, whom he succeeded. Kuang was succeeded by his brother, King Ding.

King Ding of Zhou
King Ding of Zhou (Chinese: 周定王; pinyin: Zhōu Dìng Wáng), personal name Ji Yu, was a king of the Chinese Zhou dynasty. He was a son of King Qing and brother of his predecessor, King Kuang.

He sent an official named Wangsun Man (王孫滿) to present gifts to the Chu army. He met King Zhuang of Chu.
Woleaian language
Woleaian is the main language of the island of Woleai and surrounding smaller islands in the state of Yap of the Federated States of Micronesia.  Woleaian is a Chuukic language. Within that family, its closest relative is Satawalese, with which it is largely mutually intelligible.  Woleaian is spoken by approximately 1700 people. Woleai has a writing system of its own, a syllabary based on the Latin alphabet.

Yap
Yap (Yapese: Waqab, sometimes written as Wa'ab, Waab or Waqaab) traditionally refers to an island group located in the Caroline Islands of the western Pacific Ocean, a part of Yap State. The name "Yap" in recent years has come to also refer to the state within the Federated States of Micronesia, inclusive of the Yap Main Islands and its various outer islands, the Yap Neighboring Islands. For specifying the island group, the name Yap Main Islands is most exact.
Homestead strike
The Homestead strike, also known as the Homestead steel strike, Homestead massacre, or Battle of Homestead, was an industrial lockout and strike that occurred in the United States, in 1892. It began on July 1, 1892, culminating in a battle in which strikers defeated private security agents on July 6, 1892.   
The governor responded by sending in the National Guard to protect strikebreakers. The dispute occurred at the Homestead Steel Works in the Pittsburgh-area town of Homestead, Pennsylvania, between the Amalgamated Association of Iron and Steel Workers (the AA) and the Carnegie Steel Company. The final result was a major defeat for the union strikers and a setback for their efforts to unionize steelworkers. The battle was a pivotal event in U.S. labor history.

Amalgamated Association of Iron and Steel Workers
Amalgamated Association of Iron and Steel Workers (AA) was an American labor union formed in 1876 to represent iron and steel workers. It partnered with the Steel Workers Organizing Committee of the CIO, in November 1935. Both organizations disbanded May 22, 1942, to form a new organization, the United Steelworkers.
Siegfried Köhler (conductor)
Siegfried Köhler (30 July 1923 – 12 September 2017) was a German conductor and composer of classical music. He worked as general music director of opera houses such as Hessisches Staatstheater Wiesbaden and the Royal Swedish Opera. Köhler conducted premieres of works by Hans Werner Henze and Volker David Kirchner, among others, and revived rarely performed operas. He also composed music for the stage and taught at universities of music in Cologne and Saarbrücken.

Hessisches Staatstheater Wiesbaden
The Hessisches Staatstheater Wiesbaden (Hessian State Theatre Wiesbaden), also known as the Staatstheater Wiesbaden or Theater Wiesbaden, is a German theatre located in Wiesbaden, in the German state of Hesse.  The company produces operas, plays, ballets, musicals and concerts on four stages. It has a resident orchestra, the Hessisches Staatsorchester. The theatre was inaugurated in 1894.

The theatre is the host for the annual festival Internationale Maifestspiele Wiesbaden, established in 1896 after the Bayreuth Festival.