hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Permutation group
In mathematics, a permutation group is a group G whose elements are permutations of a given set M and whose group operation is the composition of permutations in G (which are thought of as bijective functions from the set M to itself). The group of all permutations of a set M is the symmetric group of M, often written as Sym(M). The term permutation group thus means a subgroup of the symmetric group. If M = {1, 2, ..., n} then Sym(M) is usually denoted by Sn, and may be called the symmetric group on n letters.

By Cayley's theorem, every group is isomorphic to some permutation group.

The way in which the elements of a permutation group permute the elements of the set is called its group action. Group actions have applications in the study of symmetries, combinatorics and many other branches of mathematics, physics and chemistry.

Set (mathematics)
In mathematics, a set is a collection of different things; the things are called elements or members of the set and are typically mathematical objects: numbers, symbols, points in space, lines, geometric shapes, variables, or other sets.  A set may be finite or infinite. There is a unique set with no elements, called the empty set; a set with a single element is a singleton.

Mathematics typically does not define precisely what constitutes a "set" or "collection", because such a definition would have to be in terms of something else previously defined.  Instead, sets serve as foundational objects whose behavior is described by axioms modeled on intuition about collections, and then essentially all other mathematical objects are rigorously defined in terms of sets.

Set theory studies possible axiom systems and their consequences.
Since the first half of the 20th century, ZFC (Zermelo–Fraenkel set theory with the axiom of choice) has been the axiom system most commonly used.
Shalimar, Florida
Shalimar is a town in Okaloosa County, Florida, United States. It is part of the Crestview–Fort Walton Beach–Destin, Florida Metropolitan Statistical Area. The population was 737 at the 2020 census, up from 717 at the 2010 census.

Fort Walton Beach, Florida
Fort Walton Beach, often referred to by the initialism FWB, is a city in southern Okaloosa County, Florida, United States. As of the 2020 census, Fort Walton Beach had a population of 20,922. It is a principal city of the Crestview−Fort Walton Beach−Destin, Florida Metropolitan Statistical Area.

Fort Walton Beach is a year-round fishing and beach resort community. Its busiest time of the year is the summer, causing a boost to the local economy because of tourism.
Russell George (Welsh politician)
Russell Ian George (born 27 April 1974) is a Welsh politician who has been the Member of the Senedd (MS) for Montgomeryshire since the 2011 election. He formerly sat as a member of the Welsh Conservative Party, but now sits as an independent, after being suspended from the Conservative party in April 2025 pending trial for serious gambling offences.

Andrew RT Davies
Andrew Robert Tudor Davies CBE (born 28 November 1968) is a Welsh politician who has served as Member of the Senedd for the South Wales Central region since 2007.

He has previously served as Leader of the Welsh Conservative Senedd Group from 2011 to 2018 and 2021 to 2024. Both times Davies resigned due to pressure from within his party to do so. As a consequence of being leader of the Welsh Conservatives, he has served a total of four terms as Leader of the Opposition, from his first from 2011 to 2016, his second from 2017 to 2018, his third from January-March 2021 and his fourth and final from May 2021-2024.
Sachini Ayendra Stanley
Sachini Ayendra Stanley (Sinhala: සචිනි අයේන්ද්‍රා ස්ටැන්ලි) is a Sri Lankan actress and beauty pageant titleholder. She won Miss World Sri Lanka 2003 and represented her country at Miss World 2003. She currently working in the Sinhala film industry, her first film Aadaraneeya Wassaanaya directed by Senesh Dissanaike Bandara was released in 2004. She won the award for best supporting actress at Signis Sri Lanka Film Awards for her performance.

Miss World 2003
Miss World 2003 was the 53rd edition of the Miss World pageant, held at the Crown of Beauty Theatre in Sanya, China, on December 6, 2003. It was the first time that the Miss World pageant held in China.

Azra Akın of Turkey crowned Rosanna Davison of Ireland as her successor at the end of the event. It is Ireland's first victory in the history of the pageant.

106 contestants competed in this year's pageant, surpassing the previous record of 95 contestants in 2000. The pageant was hosted by Phil Keoghan, Amanda Byram, and Angela Chow. Luis Fonsi and Bryan Ferry performed in this year's pageant.
Taipei Japanese School
Taipei Japanese School (TJS) is a Japanese international school located in Shilin District, Taipei. TJS was established in 1947 and mainly serves the children (up to junior high school) of Japanese expatriates in Taiwan.

Traditionally, TJS students have returned to Japan to commence their high school education, while a minority choose to attend Taipei American School, which is located across the street. Among the TJS students who chose the latter option was Taiwanese-Japanese actor Takeshi Kaneshiro. TJS moved to its current location in Tianmu in 1983.

With the departure of many Japanese expatriate families from Taiwan during the 1990s, TJS saw its enrollment decline significantly between 1990 and 2010.   However, enrollment began to bounce back by the 2010s.

Takeshi Kaneshiro
Takeshi Kaneshiro (金城 武, Kaneshiro Takeshi; born October 11, 1973) is a Japanese actor and singer based in Taiwan. Beginning his career as a pop idol, he has since moved his focus from music to film. Kaneshiro has worked with renowned directors throughout East Asia, including Wong Kar-wai (Chungking Express and Fallen Angels), Peter Chan (Perhaps Love, The Warlords, and Dragon), Zhang Yimou (House of Flying Daggers) and John Woo (Red Cliff and The Crossing I and II), resulting in collaborations that have achieved both commercial success and critical acclaim. Kaneshiro is also well known in the gaming industry for being the model and voice for the samurai character Samanosuke Akechi in Capcom's Onimusha video game series.
Anat Zamir
Anat Zamir (Hebrew: ענת זמיר‎; 18 April 1962 – 15 December 2018) was an Israeli actress, model and beauty pageant titleholder. She was named Na'arat Israel at the Miss Israel contest of 1980 and went on to represent Israel at the Miss World 1980, contest where she was third runner-up. Zamir modelled for multiple companies and was in the 1990 film Kiss in the IDF and the 1991 film Shevet Choen.

Miss Israel
Miss Israel (also referred to as Hebrew: מיס ישראל, Malkat HaYōfî, lit. 'The Beauty Queen') was a national beauty pageant in Israel. The pageant was founded in 1950, where the winners were sent to Miss Universe.
Missionary Baptists
The Missionary Baptist church is a Christian denomination that emerged in the American South during the late 19th century. Missionary Baptists separated from the Southern Baptist Convention due to theological differences. Missionary Baptists believe in the classic tenets of the Baptist polity: the autonomy of local congregations and the view that baptism and church membership are reserved for mature congregants. The defining characteristic remains an enduring insistence on local church autonomy.

In the United States, two sizable Missionary Baptist church associations operate today: the American Baptist Association (ABA), established in 1924, and the Baptist Missionary Association of America (BMAA), established as the North American Baptist Association in 1950. The collective membership totals over a million people.

Baptist Missionary Association of America
The Baptist Missionary Association of America (BMAA) is a Christian denomination in the United States. The BMAA owns the Baptist Missionary Association Theological Seminary, with campuses in Jacksonville, Texas, Conway, Arkansas, and online. The BMAA also operates Lifeword Media Ministries and DiscipleGuide Church Resources, located in Conway, Arkansas. The missions department offices are also  located  in Conway, Arkansas.
Karachi–Peshawar Line
Karachi–Peshawar Railway Line (Urdu: کراچی–پشاور مرکزی ریل راستہ, romanized: karāčī-pešāvar markazī rēl rāsta) (also referred to as Main Line 1 or ML-1) is one of four main railway lines in Pakistan, operated and maintained by Pakistan Railways. The 1,687 kilometers (1,048 mi) long line starts at Kiamari station, Sindh, and ends at Peshawar Cantonment Station in Khyber Pakhtunkhwa. The railway is dual tracked between Keamari and Shahdara Bagh, and Chaklala and Golra Sharif. With 173 railway stations, the line serves as the country's main passenger and freight line, 75% of the country's cargo and passenger traffic passing through yearly.

In 2016, funding for a six-year, US$6.8 billion upgrade and renovation project was agreed as part of the China Pakistan Economic Corridor, with the average speed to be doubled to 140 kilometers per hour upon completion. The project has been delayed several times since then.

Golra Sharif
Golra Sharif (Urdu: گولڑہ شریف) is a town situated near the Margalla Hills in Islamabad Capital Territory, Pakistan, at about 520 m (1,710 ft) above sea level, 17 km (11 mi) from the ancient city of Taxila.

It is known for the Mausoleum of Meher Ali Shah that yearly attracts thousands of devotees. Prior to the arrival of Meher Ali Shah's ancestors, Golra Sharif was a village in the suburbs of Rawalpindi.
Pierre-Simon Girard
Pierre-Simon Girard (4 November 1765 – 30 November 1836) was a French mathematician and engineer, who worked on fluid mechanics.

Girard was born in Caen.  A prodigy who invented a water turbine at the age of ten, he worked as an engineer at the École Nationale des Ponts et Chaussées. He was in charge of planning and construction of the Amiens canal and the Ourcq canal. He collaborated with Gaspard de Prony on the Dictionnaire des Ponts et Chaussées (Dictionary of Bridges and Highways,  1787). He wrote on fluids, and in 1798 he published a monograph, Traité analytique de la résistance des solides on beam theory, including possibly its first history, within the topic of strength of materials. The complicated beam equations were not of practical much use, since he applied Euler's non-linear theory. In 1799, he and other engineers and scientists accompanied Napoleon on his expedition to Egypt. He died in Paris, aged 71.

Gaspard de Prony
Baron Gaspard Clair François Marie Riche de Prony (22 July 1755 – 29 July 1839) was a French mathematician and engineer, who worked on hydraulics. He was born at Chamelet, Beaujolais, France and died in Asnières-sur-Seine, France.
Perittodus
Perittodus is an extinct genus of four-limbed stem-tetrapod from the Mississippian (mid-Tournaisian) of Scotland. It contains a single species, Perittodus apsconditus, based on disarticulated skull and postcranial bones from the Ballagan Formation. The lower jaw of the holotype specimen was about 6.8 cm (2.7 in.) in length and had a pattern of dentition similar to the Devonian taxon Ymeria. Perittodus was described in a 2016 study which was devised to fill in the tetrapod and stem-tetrapod faunas of Romer's gap, an interval of the early Carboniferous with few vertebrate fossils. It was one of five new genera named in this study, along with Aytonerpeton, Diploradus, Koilops, and Ossirarus.

Ymeria
Ymeria is an extinct genus of early stem tetrapod from the Devonian of Greenland. Of the two other genera of stem tetrapods from Greenland, Acanthostega and Ichthyostega, Ymeria is most closely related to Ichthyostega, though the single known specimen is smaller, the skull about 10 cm in length. A single interclavicle resembles that of Ichthyostega, an indication Ymeria may have resembled this genus in the post-cranial skeleton.
Chase Purdy
Charles Russell  "Chase" Purdy III (born November 11, 1999) is a former American professional stock car racing driver. He most recently competed full-time in the NASCAR Craftsman Truck Series, driving the No. 77 Chevrolet Silverado for Spire Motorsports.

He competed for MDM Motorsports in the Truck and ARCA Racing Series, David Gilliland Racing in the NASCAR K&N Pro Series East, and Anthony Campi Racing in super late model racing. Purdy was named to the 2017–2018 and 2018–2019 NASCAR Next classes.

Late model
Late Model stock car racing, also known as late model racing and late models, refers to a type of auto racing that involves purpose-built cars simultaneously racing against each other primarily on oval tracks.  This type of racing was early-on characterized by its participants' modification to the engines of post-World War II passenger cars, but the modern day understanding references a class that allows considerable modifications to both the engine and body, yet requires some form of front fender package.
Tan Ruisong
Tan Ruisong (Chinese: 谭瑞松; born February 1962) is a former Chinese executive and engineer. He was investigated by China's top anti-graft agency in August 2024. Previously he served as chairman and party branch secretary of the Aviation Industry Corporation of China, China's dominant aircraft maker. He was a member of the 13th National Committee of the Chinese People's Political Consultative Conference.

Aviation Industry Corporation of China
The Aviation Industry Corporation of China (AVIC) is a Chinese state-owned, publicly-traded aerospace and defense conglomerate headquartered in Beijing. AVIC is overseen by the State-owned Assets Supervision and Administration Commission of the State Council. It is ranked 140th in the Fortune Global 500 list as of 2021, and has over 100 subsidiaries, 27 listed companies and 500,000 employees across the globe. AVIC is also the sixth largest defense contractor globally as of 2022 and second largest Chinese defense contractor with total revenue of $79 billion (from both defense and non-defense services).
Underdogs (TV series)
Underdogs is a 2006 Canadian television series spin-off from Marketplace. Host Wendy Mesley brings together three people, the underdogs, who have a consumer complaint to help them win their way against three companies of Canada.

Marketplace (Canadian TV program)
Marketplace (officially CBC News: Marketplace) is a Canadian investigative consumer program which has been broadcast on CBC Television since 1972. The program  investigates consumer reports on issues such as product testing, health and safety, fraudulent business practices, and also tests government and industry promises.

Despite airing on Friday nights, which typically have low viewership, the show has had high ratings and achieved over 1 million viewers for some episodes. In 2012, it was the fifth-highest rated show on CBC.
Greenlight Bookstore
Greenlight Bookstore is a Brooklyn independent bookstore on Fulton Street in Fort Greene. Established by Rebecca Fitting and Jessica Stockton-Bagnulo in 2009, it sells books in several genres, hosts events with authors, and is a partner of the Brooklyn Academy of Music. Originally, the bookstore had a second location in Prospect Lefferts Gardens, which closed in May of 2023 due to financial difficulties.

Brooklyn Academy of Music
The Brooklyn Academy of Music (BAM) is a multi-arts center in Brooklyn, New York City. It hosts progressive and avant-garde performances, with theater, dance, music, opera, film programming across multiple nearby venues.

BAM was chartered in 1859, presented its first show in 1861, and began operations in its present location in Fort Greene, Brooklyn, in 1908. The Academy is incorporated as a New York State not-for-profit corporation. It has 501(c)(3) status.
Ronny Nilsen
Ronny Nilsen (born 7 May 1971 in Åsane, Bergen) is a former Norwegian track and field athlete who competed in the javelin. He represented the Hordaland club IL Norna-Salhus. He was a policeman in Oslo for many years, but since 1 September 2008 he is the head of sport of Norges Friidrettsforbund.

He took part in the 2004 Olympics in Athens, 2005 World Championships in Helsinki and the 2006 European Athletics Championships in Gothenburg, but failed to get past the qualification rounds.

Nilsen has a personal best of 84.73 meters (278.0 ft), which places him third on the Norwegian all-time list, behind Andreas Thorkildsen and Pål Arne Fagernes. He competed for the club IL Norna-Salhus.

Nilsen is a graduate of the Norwegian Police University College, and for many years worked at the Sentrum politistasjon in Oslo. After a period as senior advisor at NAV, he found a job as the head of sport at Norges Friidrettsforbund.

IL Norna-Salhus
Idrettslaget Norna-Salhus is a Norwegian athletics club from Salhus in Åsane, Bergen

It was founded on 14 October 1935. The club originally had an association football section as well, but it split away in 1987 to form FK Bergen Nord.

Since this split Norna-Salhus gradually rose to prominence in national athletics, especially within the jumping section. Triple jumpers Sigurd Njerve and Ketill Hanstveit established Norwegian records. Other athletes such as decathlete Benjamin Jensen, race walkers Kjersti Plätzer and Erik Tysse, hammer thrower Mona Holm, and jumper Oda Utsi Onstad have later joined Norna-Salhus.
Public housing estates in Ngau Tau Kok and Kowloon Bay
The following shows the public housing estates (including Home Ownership Scheme (HOS), Private Sector Participation Scheme (PSPS), Tenants Purchase Scheme (TPS)) in Ngau Tau Kok, Jordan Valley, Kowloon Bay and surrounding neighbourhoods, in Kwun Tong District, Kowloon, Hong Kong.

Choi Hung Estate
Choi Hung Estate (Chinese: 彩虹邨; lit. 'rainbow estate') is a public housing estate in Ngau Chi Wan, Kowloon, Hong Kong. It was built by the former Hong Kong Housing Authority (屋宇建設委員會) and is now managed by the current Hong Kong Housing Authority. It received a Silver Medal at the 1965 Hong Kong Institute of Architects Annual Awards.
Ohio State Route 823
State Route 823 (SR 823), officially known as the Southern Ohio Veterans Memorial Highway and colloquially as the Portsmouth Bypass, is a north–south four-lane divided controlled-access highway in Scioto County, Ohio. The highway, which runs from Sciotodale to Lucasville, reroutes through traffic around the cities of Portsmouth and New Boston to the east. The bypass provides better mobility within the local area for residents and has the potential to increase the economic development of the local area. In September 2013, the Ohio Department of Transportation (ODOT) recommended a public–private partnership (P3) to fund and build the highway.  Construction began in June 2015. The highway was dedicated on December 13, 2018 with vehicle traffic beginning the next day.

Lucasville, Ohio
Lucasville is a census-designated place (CDP) in Scioto County, Ohio, United States. The population was 1,655 at the 2020 census. It is part of the Portsmouth micropolitan area.

Lucasville is the location of the Scioto County Fairgrounds. The Southern Ohio Correctional Facility, one of Ohio's three maximum security prisons and the location of Ohio's death house where death row inmates are executed, is located just outside Lucasville. The community is served by the Portsmouth Public Library, as well as the Valley Local School District and Northwest Local School District.
Aptos Creek
Aptos Creek is a southward flowing 9.5 miles (15.3 km) creek that begins on Santa Rosalia Mountain on the southwestern slope of the Santa Cruz Mountains in Santa Cruz County, California and enters Monterey Bay, at Seacliff State Beach in Aptos, California.

Santa Cruz Mountains
The Santa Cruz Mountains (Mutsun Ohlone: Mak-sah-re-jah, "Sharp Ridged Mountain of the Eagle" or "People of the Eagle Mountain") are a mountain range in central and Northern California, United States, constituting a part of the Pacific Coast Ranges. They form a ridge down the San Francisco Peninsula, south of San Francisco. They separate the Pacific Ocean from the San Francisco Bay and the Santa Clara Valley, and continue south to the Central Coast, bordering Monterey Bay and ending at the Salinas Valley. The range passes through the counties of San Mateo, Santa Clara, and Santa Cruz, with the Pajaro River forming the southern boundary.
Tom Herrion
Tom Herrion (born November 13, 1967) is an American college basketball assistant coach for South Florida. He also previously served as head basketball coach at Marshall University and at the College of Charleston.

Jamie Dixon
James Patrick Dixon II (born November 10, 1965) is an American college basketball coach who is the head coach of the TCU Horned Frogs men's team, where he played college ball. He previously served as the head coach of the University of Pittsburgh men's basketball team from 2003 through 2016.

In 2009, he was the head coach for the FIBA Under-19 2009 gold-medal winning United States national basketball team for which he was named the 2009 USA Basketball National Coach of the Year. Dixon was named Big East Coach of the Year in 2004, Naismith College Coach of the Year in 2009,  Jim Phelan National Coach of the Year in 2010, and the Sporting News National Coach of the Year award in 2011. Dixon played college basketball at Texas Christian University, was selected by the Washington Bullets in the 1987 NBA draft, and played professionally with the Continental Basketball Association's Lacrosse Catbirds and for Hawke's Bay Hawks of the New Zealand National Basketball League.
The Dark Horse (1946 film)
The Dark Horse is a 1946 American drama film directed by Will Jason and written by Charles R. Marion and Leo Solomon. The film stars Phillip Terry, Ann Savage, Allen Jenkins, Jane Darwell, Donald MacBride and Edward Gargan. The film was released on July 19, 1946, by Universal Pictures.

Jane Darwell
Jane Darwell (born Patti Woodard; October 15, 1879 – August 13, 1967) was an American actress of stage, film, and television. With appearances in more than 100 major movies spanning half a century, Darwell is perhaps best remembered for her poignant portrayal of the matriarch and leader of the Joad family in the film adaptation of John Steinbeck's The Grapes of Wrath, for which she received the Academy Award for Best Supporting Actress. She has a star on the Hollywood Walk of Fame.
Maria Antónia Palla
Maria Antónia Palla (born 10 January 1933) is a Portuguese journalist, writer and feminist who was one of the first female journalists in Portugal. She played an important role in the legalization of abortion in the country, by promoting the practice in interviews and television programmes. In 2004 Palla was awarded the title of Commander of the Order of Liberty. She is the mother of António Costa, the former Prime Minister of Portugal.

Order of Liberty
The Order of Liberty, or the Order of Freedom (Portuguese: Ordem da Liberdade), is a Portuguese honorific civil order that distinguishes relevant services to the cause of democracy and freedom, in the defense of the values of civilization and human dignity. The order was created in 1976, after the Carnation Revolution of 1974 in which the corporatist authoritarian Estado Novo regime of António de Oliveira Salazar and Marcello Caetano was deposed. The Grand Collar can also be given by the President of Portugal to former Heads of State and others whose deeds are of an extraordinary nature and particular relevance to Portugal, making them worthy of such a distinction. This can include political acts, physical acts of defense for Portugal, or the good representation of Portugal in other countries.