OpenLLM-France/wikimedia huggingface dataset:
# Hopf algebra of permutations

In algebra, the Malvenuto–Poirier–Reutenauer Hopf algebra of permutations or MPR Hopf algebra is a Hopf algebra with a basis of all elements of all the finite symmetric groups S$_n$, and is a non-commutative analogue of the Hopf algebra of symmetric functions. It is both free as an algebra and graded-cofree as a graded coalgebra, so is in some sense as far as possible from being either commutative or cocommutative. It was introduced by Malvenuto & Reutenauer (1995) and studied by Poirier & Reutenauer (1995).

## Definition

The underlying free abelian group of the MPR algebra has a basis consisting of the disjoint union of the symmetric groups S$_n$ for n = 0, 1, 2, .... , which can be thought of as permutations.
The identity 1 is the empty permutation, and the counit takes the empty permutation to 1 and the others to 0.
The product of two permutations (a$_1$,...,a$_m$) and (b$_1$,...,b$_n$) in MPR is given by the shuffle product (a$_1$,...,a$_m$) ш (m + b$_1$,...,m + b$_n$).
The coproduct of a permutation a on m points is given by Σ$_{a=b*c}$ st(b) ⊗ st(c), where the sum is over the m + 1 ways to write a (considered as a sequence of m integers) as a concatenation of two sequences b and c, and st(b) is the standardization of b, where the elements of the sequence b are reduced to be a set of the form {1, 2, ..., n} while preserving their order.
The antipode has infinite order.

## Relation to other algebras

The Hopf algebra of permutations relates the rings of symmetric functions, quasisymmetric functions, and noncommutative symmetric functions, (denoted Sym, QSym, and NSym respectively), as depicted the following commutative diagram. The duality between QSym and NSym is shown in the main diagonal of this diagram.
# Hotu-iti

Hotu-iti (also, "Tongariki territory") is an area of southeastern Easter Island that takes its name from a local clan. Located in Rapa Nui National Park, the area includes Rano Raraku crater, the Ahu Tongariki site, and a small bay. In the 15th and 16th centuries, the Hotu-iti clan was one of two polities on Easter Island.

## Geography

Hotu-iti contains Rano Raraku crater, which is the island's only source of a type of stone that was considered to be the best for carving statues; it was also a source of moss which was used for canoe caulking. Hotuiti Bay, a small cove, is protected by the cliffs of the Poike Peninsula. According to local legend, the god Tangaroa was killed in the bay and was buried in the vicinity. The Rano Raraku cliffs and quarry stand above Hotu-iti. The landscape has been described as a "wondrous spiritual landscape of striking beauty".

## History

In the 15th and 16th centuries, the island was divided into two polities, described as either west (Tu'u) and east (Hotu-iti) confederacies, with Hotu-iti being the lower ranked; or northern (Tu'u Aro) and southern (Hotu-iti). In 1960, a tsunami, approximately 6 metres (20 ft) above sea level, crossed 500 metres (1,600 ft) of Hotu-iti, sweeping away ahu and moai (statues), and scattering them by 50–150 metres (160–490 ft). Fifteen statues of Hotu-iti's Ahu Tongariki site were damaged; a team of Japanese archaeologists restored the site between 1992 and 1994.

## Leadership

In Polynesian mythology, Hotu-iti was the youngest and favourite son of Hotu Matu'a, the legendary first settler of Easter Island. One of the known chiefs of the Hotu-iti clan was Kainga, said to be a descendant of the sixth son of the first king who "proved himself a valiant warrior." He had a son who succeeded him named Huriavai. The Tupahotu, Koro-Orongo and Ure-o-Hei clans were considered part of the Hotu-iti clan.
# House of Nassau-Hadamar

Nassau-Hadamar is the name of two side lines of the Ottonian main line of the House of Nassau. The older line of the counts of Nassau-Hadamar existed from 1303 to 1394; the younger line existed from 1607 to 1711 and received the hereditary title of prince in 1652.

## Nassau-Hadamar (Older Line)
### Emergence

After the death of Henry II the Rich of Nassau his sons, Walram II and Otto I shared the inheritance in 1255. The boundary between the two territories was formed approximately by the River Lahn. Walram took over the southern part of the realm (Walramic main line) and Otto, the northern part (Ottonian main line). The marriage between Otto and Agnes of Leiningen gave the Ottonian main line suzerainty over the March of Hadamar.
Otto's death in 1290 led to repeated inheritance disputes among his sons. In 1303, they shared his estate, under the mediation of John I of Limburg. The eldest son Henry took over the sub-county of Nassau-Siegen with its estate in the Siegerland and the Barony of Westerwald, the second son Emich/Emicho I inherited the sub-county of Nassau-Hadamar with Driedorf and Esterau, and the third son, John the sub-county of Nassau-Dillenburg with its estates around Dillenburg, Herborn, Mengerskirchen, the Calenberg Tithe and the jurisdiction (Gericht) of Heimau.

### Regents

* John Louis of Nassau-Hadamar (1620–1653), became prince in 1650
* Maurice Henry of Nassau-Hadamar (1653–1679)
* Francis Alexander of Nassau-Hadamar (1679–1711)
** Wardship by Francis Bernard of Nassau-Hadamar (1679–1694)
** Divided between other Ottonian-Nassau houses (1712–1742)
* William Hyacinth of Nassau-Siegen (1742–1743)
** Nassau-Hadamar falls entirely to Orange-Nassau.

## Literature

* Hellmuth Gensicke (1999), Landesgeschichte des Westerwaldes (in German) (3rd ed.), Wiesbaden: Historische Kommission für Nassau, ISBN 3-922244-80-7
* Walter Rudersdorf (1967), Gemeinde Ellar/Westerwald (ed.), Im Schatten der Burg Ellar (in German), Frankfurt am Main: Waldemar Kramer
* Jacob Wagner: Die Regentenfamilie von Nassau-Hadamar: Geschichte des Fürstenthums Hadamar mit besonderer Rücksicht auf seine Kirchengeschichte, von den ältesten Zeiten bis auf unsere Tage, nach Urkunden bearbeitet, Mechitharisten, 1863 (Band 1: Google Books, Band 2: Google Books)
# Howard Glenn

Howard Earl Glenn (September 26, 1934 – October 9, 1960) was an American gridiron football player. He played collegiately at Linfield College and professionally with the Hamilton Tiger-Cats of the Canadian Football League (CFL) and in the American Football League (AFL). He was the only AFL player to die from injuries sustained in a regular season football game.
Glenn was born in Vancouver, Washington, and played high school football in Louisville, Mississippi. At Linfield College in McMinnville, Oregon, he played tight end and in 1956 caught a 75-yard touchdown pass. He was named to the all-Northwest Conference team in 1957.
In 1960, the AFL's inaugural season, Glenn joined the AFL New York Titans as an offensive guard. Glenn sustained a broken neck in the first half during a game vs. the Houston Oilers on October 9, 1960, at Jeppesen Stadium and died later that day.
# Hromádka

Hromádka is a Czech surname. Notable people with the surname include:
* Eduard Hromádka (1909–1966), Czech alpine skier
* Josef Hromádka (1889–1969), Czech Protestant theologian
* Karel Hromádka (1887–1956), Czech chess player
# Huallaga River Boats Collision (2021)

The Huallaga river boats collision was a fatal boat collision that killed 21 in Peru. It occurred on August 29, 2021, in the Alto Amazonas Province, west of the Department of Loreto. An additional unknown number of people were described as missing.

## Description

The event occurred in the early morning of August 29 in the Alto Amazonas Province, when a motorized ferry collided with a river boat. The boat had approximately 80 people on board. Intense morning fog made it difficult to see.
Petroperú reported that the 80-person boat was called Ayachi, and the motor boat Nauta. Ayachi picked up its passengers at 1:00 a.m. in Santa María to transfer them to Yurimaguas, while Nauta headed for Iquitos. Ayachi's passengers belonged to an evangelical congregation called Nueva Jesuralén.

## Rescue

At the time of the accident, smaller boats of locals came to rescue the survivors. A passenger from Ayachi relates:
"Some grabbed us from behind, desperate. We were under the boat. We have managed to get out. My colleagues don't. I have lost my wife and seven-year-old son."
Rescuers from the Peruvian National Police and the Peruvian Navy went to the scene, where they managed to rescue 50 people alive. At the beginning, 16 were reported missing.
The number of survivors rose to 60, and the number of deceased increased to 23 on August 31. One family was reported to have 14 deaths in the accident.
# Hubert Kingston

Hubert Ernest Kingston (15 August 1876 – 9 June 1955) was an English cricketer. Kingston was a right-handed batsman who bowled leg break. He was born at Northampton, Northamptonshire, and was educated at Blair Lodge School in Scotland.
Kingston made his debut for Northamptonshire against Staffordshire in the 1895 Minor Counties Championship. He played minor counties cricket for Northamptonshire for the next decade, making a total of 57 appearances. Having won the 1903 and 1904 Minor Counties Championship, Northamptonshire were granted first-class status for the 1905 season, allowing them to take part in the County Championship. He made his first-class debut in Northamptonshire's inaugural first-class fixture against Hampshire at the County Ground, Southampton. He made twelve further first-class appearances for the county, the last of which came in the 1906 County Championship against Nottinghamshire. In his thirteen first-class matches, he scored 335 runs at an average of 15.95, with a high score of 68. This score was his only half century and came on debut against Hampshire. With the ball, he took 6 wickets at a bowling average of 41.00, with best figures of 2/8.
He died at Long Buckby, Northamptonshire, on 9 June 1955. His brothers, Charles, Frederick, James and William, all played first-class cricket.
# Huichihuayan

Huichihuayan is a town located in the Huehuetlán municipality in the southeast region of San Luis Potosí, Mexico. With a population of over 2,000, it is the largest town in its municipality.
# Hu Ning

Hu Ning (simplified Chinese: 胡宁; traditional Chinese: 胡寧; 1916–1997) was a Chinese physicist and writer.

## Biography

Hu was born in Suqian, Jiangsu, China on 11 February 1916. From 1928 to 1934, Hu studied at the Zhenjiang High School (镇江中学) in Zhenjiang, and Suzhou High School in Suzhou. In 1935, Hu studied at the physical department of Zhejiang University in Hangzhou, Zhejiang. From 1935 to 1937, Hu studied in the department of physics at Tsinghua University in Beijing, where he graduated in 1938.
After his graduation from Tsinghua, Hu became the teaching assistant for his professor Zhou Peiyuan in the department of physics.
In 1940, Hu examed and won the Boxer Indemnity Scholarship Program. In 1941, Hu went to study in the United States. Hu studied fluid mechanics at the California Institute of Technology. His doctoral advisor was Theodore von Kármán. Hu also studied quantum mechanics under Paul Sophus Epstein during this period. Hu obtained his PhD in 1943 from Caltech.
From 1944 to 1945, Hu stayed at the Institute for Advanced Study in Princeton, New Jersey, and studied quantum field theory and basic particles theories under Wolfgang Pauli. From 1946 to 1949, Hu visited Europe. He worked at the Dublin Institute for Advanced Studies in Dublin, Ireland between 1946 and 1948. During this time he also visited the Niels Bohr Institute in Copenhagen. Hu went back to the United States, and from 1949 to 1950, Hu did research at the nuclear physics department of the Cornell University, New York.
In 1950, invited by the physicist Ta-You Wu (at that time, Wu headed the Theoretical Physics Division of the Canadian National Research Council), Hu went to Canada, and did research and lectured there.
In 1951, Hu accepted the invitation from Peking University in Beijing, and went back to China. Hu was a long-time professor in the department of physics at Peking University. Since 1953, Hu was a researcher at the Institute of Modern Physics (近代物理研究所) and the Institute of Nuclear Physics (原子能研究所) of the Chinese Academy of Sciences. From 1956 to 1959, Hu was a researcher and group leader at the Joint Institute for Nuclear Research, USSR. Since 1980, Hu was a researcher at the Institute of Theoretical Physics (理論物理研究所) of the Chinese Academy of Sciences in Beijing.
Hu was elected academician of the Chinese Academy of Sciences in 1955. Hu was appointed the first director-general of Peking University Research Institute of Theoretical Physics (北京大學理論物理研究所).
Hu died in Beijing on 16 December 1997.

## Publications

Hu wrote or edited some earliest textbooks of relativity and quantum physics in China, which are still in use:
* 《電動力學》 (Electrodynamics); 1963
* 《场的量子理论》 (Quantum Field Theory); 1964
* 《廣義相對論和引力場理論》 (General Relativity and Gravitation); ISBN 7-03-007835-7; republished in 2000
# Hulaco, Alabama

Hulaco is an unincorporated community located in extreme southeastern Morgan County, Alabama, United States, and is included in the Decatur Metropolitan Area, as well as the Huntsville-Decatur Combined Statistical Area. A post office operated under the name Hulaco from 1855 to 1904
# Humaitã River

The Humaitã River, also known as the Turvo River, is a river of Rio Grande do Sul state in southern Brazil. It is a tributary of the Da Prata River.
# Hustler Video

Hustler Video is an American independent pornographic film studio. It is owned by Larry Flynt's Larry Flynt Publications, and is part of its Hustler-branded range of enterprises, which includes Hustler magazine, the Hustler Casino and the Hustler Hollywood retail outlets. In 2003 Hustler Video bought VCA Pictures, which maintains a separate brand identity within the LFP conglomerate.
Hustler Video is known for their parodies of mainstream movies, and of celebrities, like Paris Hilton, David Hasselhoff or Lindsay Lohan, and TV shows, like "Happy Days", "Star Trek" and "Glee". In response to 2008 Republican presidential nominee John McCain selecting Alaska governor Sarah Palin as his running mate, Hustler placed a classified ad on Craigslist, seeking a Sarah Palin doppelgänger willing to star in a pornographic film while portraying the governor. The film, Who's Nailin' Paylin, was released November 4, 2008 eventually starring Lisa Ann.

## Awards

The following is a selection of some of the major pornography awards the studio has won.
* 2002 AVN Award - 'Best All-Sex DVD' for Porno Vision
* 2002 AVN Award - 'Best All-Sex Film' for Porno Vision
* 2002 AVN Award - 'Top Selling Release of the Year' for Snoop Dogg's Doggystyle
* 2003 AVN Award - 'Best Ethnic-Themed Release' for Liquid City
* 2003 AVN Award - 'Best Art Direction - Film' - Kris Kramski for America XXX
* 2003 AVN Award - 'Best Vignette Series for Barely Legal
* 2004 AVN Award - 'Best Vignette Series for Barely Legal
* 2004 AVN Award - 'Top Selling Release of the Year' for Snoop Dogg's Hustlaz: Diary of a Pimp
* 2004 AVN Award - 'Best Ethnic-Themed Release - Black' for Snoop Dogg's Hustlaz: Diary of a Pimp
* 2005 AVN Award - 'Best Amateur Release' for Adventure Sex
* 2005 AVN Award - 'Best All-Sex Release' for Stuntgirl
* 2006 AVN Award - 'Best All-Sex Release' for Squealer
* 2007 AVN Award - 'Best Pro-Am or Amateur Series' for Beaver Hunt
* 2008 AVN Award - 'Best Interactive DVD' for InTERActive
* 2008 AVN Award - 'Best Vignette Series for Barely Legal School Girls
* 2009 AVN Award - 'Best Specialty Series - Other Genre' for Taboo
* 2009 AVN Award - 'Clever Title of the Year' for Strollin in the Colon
* 2010 XBIZ Award - 'Parody Release of the Year' for Not the Bradys XXX: Marcia
* 2011 XBIZ Award - 'Best Art Direction' for This Ain't Avatar XXX 3D
* 2011 XBIZ Award - 'Marketing Campaign of the Year' for This Ain't Avatar XXX
* 2012 XBIZ Award - 'Parody Studio of the Year'
* 2013 XBIZ Award Nominee - 'Studio of the Year', 'Parody Release of the Year-Comedy' for This Ain't Nurse Jackie XXX; Additional nominations include: 'Vignette Release of the Year' for Barely Legal 124 and 'Vignette Series of the Year' for Barely Legal and 'All-Girl Series of the Year' for My First Lesbian Experience
* 2014 AVN Award — Best Retail Chain – Large
* 2014 XBIZ Award - 'Vignette Release of the Year' for Busty Beauties Car Wash

## Legal issues

In 2011, Hustler Video was fined $14,175 in workplace safety charges for three separate complaints: a failure to provide protective devices to workers, failure to maintain proper health policies, and failure to provide vaccinations to workers.
# Hypocrates

Hypocrates may refer to:
* misspelling of Hippocrates
* Hypocrates (song), by Welsh singer Marina Diamandis
# Hurumu

Hurumu is one of the woredas in the Oromia Region of Ethiopia. It was part of Yayu woreda. The major town is Hurumu.

## Demographics

The 2007 national census reported a total population for this woreda of 42,667, of whom 21,309 were men and 21,358 were women; 4,519 or 10.59% of its population were urban dwellers. The majority of the inhabitants practised Ethiopian Orthodox Christianity, with 41.35% of the population reporting they observed this belief, while 34.32% of the population said they were Muslim, and 24.24% were Protestant.
# Hyenas Only Laugh for Fun

Hyenas Only Laugh for Fun is the third solo album by singer Roger Chapman and his band The Shortlist. The album was released 1981.

## Track listing

All lyrics by Roger Chapman

### Side one

* "Prisoner" (Chapman, Tim Hinkley, Geoff Whitehorn) – 5:38
* "Hyenas Only Laugh for Fun" (Chapman, Hinkley, Whitehorn, Jerome Rimson) – 3:10
* "Killing Time" (Chapman) – 5:35
* "Wants Nothing Chained (Chapman, Whitehorn)– 3:00
* "The Long Goodbye" (Chapman) – 4:39

### Side two

* "Blood and Sand" (Chapman, Whitehorn) – 4:55
* "Common Touch" (Chapman) – 5:10
* "Goodbye Reprise" (Chapman) – 1:10
* "Hearts On The Floor" (Chapman) – 4:30
* "Step Up – Take A Bow" (Chapman, Whitney) – 3:30
* "Jukebox Mama" (Chapman, Troy Seals) – 1:22

## Personnel

* Roger Chapman – Harmonica, vocals
* Tim Hinkley – Keyboards
* Geoff Whitehorn – Guitars
* Steve Simpson – Violin, mandolin, slide guitar
* Jerome Rimson – Bass guitar
* John Wetton – Bass guitar
* Leonard "Stretch" Stretching – Drums
* Alan Coulter – Drums
* Nick Pentelow – Saxophones
* Poli Palmer – Synthesisers, programming
* Raymond Burrell – Editing blocks
* Duncan Kinnell – Percussion
* Jill Mumford - sleeve design
# Hydride telluride

Hydride tellurides are mixed anion compounds containing both hydride and telluride ions. They are in the category of heteroanionic chalcogenides, or mixed anion compounds. Related compounds include the oxyhydrides, hydride sulfides, and hydride selenides.

## Formation

Salt-like hydride tellurides may be formed by heating tellurium with a metal hydride in an oxygen-free capsule at around 700°C with a caesium chloride flux to assist in crystal formation. For rare earth elements, this method works as long as tellurium has enough oxidising power to convert a +2 oxidation state to a +3 state. So for samarium, europium, thulium and ytterbium it does not work as the monotelluride is more stable with the metal in a +2 oxidation state. Also scandium and lutetium atoms are too small.
    LaH$_3$ + Te → LaHTe + H$_2$
Tellurido-hydrido-transition metal complexes are known. They are formed by heating metal hydrido complexes with tellurium.
    L$_2$MH$_3$ + 2 Te → L$_2$M(Te$_2$)H + H$_2$
    L$_2$MH$_3$ + Te → L$_2$M(=Te)H + H$_2$
where L and M represent ...

## Properties

With rare earth elements the hydride tellurides all have the same structure as the small or heavy rare-earth elements. Six selenium ions are arranged in a trigonal prism around the rare-earth atom. The rectangular faces are capped with hydride ions. Bond lengths are about the same as for binary tellurides and hydrides.
When heated to 1100°C, rare-earth hydride tellurides decompose to a monotelluride:
   2LaHTe → 2LaTe + H$_2$

## List

Some hydride tellurides, with details of crystal structure :
| Formula | Crystal system | Space group | Unit cell (in angstroms) | Volume | Density | Notes |
| [η$^1$-3,5-tBu$_2$pz(η-Al)H)$_2$Te]•CH$_3$C$_6$H$_5$ pz=pyrazolato | monoclinic | P2$_1$/n | a=12.288 b=15.592 c= 18.031 β=106.29° Z=4 | 3316.1 | 1.270 | melt 250°C; colourless |
| YHTe | hexagonal | P6m2 | a=4.0095 c=4.1547 Z=1 | | | pale grey; water insensitive |
| (t-BuC$_5$H$_4$)$_2$Nb(η$^2$-Te$_2$)H | | | | | | dark orange |
| [(C$_5$Me$_5$)$_2$Nb(Te$_2$)H] ?? | | | | | | |
| (tBuC$_5$H$_4$)$_2$Nb(Te$_2$)H·Cr(CO)$_5$ | | | | | | |
| {(tBuC$_5$H$_4$)$_2$NbH(Te)$_2$}Fe$_2$(CO)$_6$ | | | | | | |
| {(tBuC$_5$H$_4$)$_2$NbH(Te)$_2$Fe$_2$(CO)$_6$}·Cr(CO)$_5$ | | | | | | |
| Mo(PMe$_3$)$_4$(η$^2$-Te$_2$)H$_2$ | monoclinic | P2$_1$/n | a=9.623 b=15.297 c=16.504 β=98.31° Z=4 | 2400 | | black |
| LaHTe | hexagonal | P6m2 | a=4.220 c=4.3914 Z=1 | | | pale grey |
| CeHTe | hexagonal | P6m2 | a=4.1756 c=4.3403 Z=1 | | 6.81 | pale grey |
| PrHTe | hexagonal | P6m2 | a=4.1461 c=4.3130 Z=1 | | | pale grey |
| NdHTe | hexagonal | P6m2 | a=4.1162 c=4.2897 Z=1 | | | pale grey |
| GdHTe | hexagonal | P6m2 | a=4.0413 c=4.2048 Z=1 | | | pale grey |
| TbHTe | hexagonal | P6m2 | a=4.0233 c=4.1639 Z=1 | | | pale grey |
| DyHTe | hexagonal | P6m2 | a=3.9984 c=4.1598 Z=1 | | | pale grey |
| HoHTe | hexagonal | P6m2 | a=3.9813 c=4.1489 Z=1 | | | pale grey |
| ErHTe | hexagonal | P6m2 | a=3.9659 c=4.1072 Z=1 | | 8.78 | pale grey |
| Cp*$_2$Ta(Te$_2$)H Cp*2Ta=permethyltantalocene | | | | | | yellow |
| Cp*$_2$Ta(Te)H | | | | | | |
| W(PMe$_3$)$_4$(η$^2$-Te$_2$)H$_2$ | | | | | | |
# Hygrotus artus

Hygrotus artus is a species of beetle in the family Dytiscidae. It is known to only occur in Inyo and Mono counties, California, United States. Its common name is the Mono Lake diving beetle.
It was previously thought to be extinct, but recent work has shown that it is neither "extinct nor living in the alkaline Mono Lake."
# Hygrotus impressopunctatus

Hygrotus impressopunctatus is a species of Dytiscidae native to Europe.
# Hygrotus inaequalis

Hygrotus inaequalis is a species of Dytiscidae native to Europe.
# Hurt Park

Hurt Park may refer to:
* Hurt Park (Atlanta), a public park in Atlanta
* Hurt Park, Roanoke, Virginia, a neighborhood in Roanoke, Virginia