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Carl Kostka
Carl Gottfried Franz Albert Kostka (3 December 1846 in Lyck – 28 December 1921 in Insterburg) was a mathematician who introduced Kostka numbers in 1882. He lived and worked in Insterburg. See also *Kostka polynomial In mathematics, Kostka polynomials, named after the mathematician Carl Kostka, are families of polynomials that generalize the Kostka numbers. They are studied primarily in algebraic combinatorics and representation theory. The two-variable Ko ... References * 19th-century German mathematicians 20th-century German mathematicians 1846 births 1921 deaths People from Ełk Members of the German National Academy of Sciences Leopoldina {{mathematician-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ełk
Ełk (; former pl, Łek; german: Lyck; Old Prussian: ''Luks''; lt, Lukas), also spelled Elk in English, is a small city in northeastern Poland with 61,677 inhabitants as of December 2021. It was assigned to Warmian-Masurian Voivodeship in 1999, after belonging to Suwałki Voivodeship from 1975 to 1998. Ełk is the seat of Ełk County. It lies on the shore of Ełk Lake, which was formed by a glacier, and is surrounded by extensive forests. It is the largest city and unofficial capital of historical Masuria. One of the principal attractions in the area is legal hunting. History Middle Ages The area where the town of Ełk is located was originally inhabited by Jatvingians, a Baltic peoples, during the early middle ages. By 1281, Skomand (Lithuanian: ''Skalmantas'') the last leader of the pagan Jatvingians, capitulated to the crusading Teutonic Knights, who initially were invited in 1226 by Konrad I of Masovia from the Polish Piast dynasty to put an end to the constant pagan rai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Insterburg
Chernyakhovsk (russian: Черняхо́вск) – known prior to 1946 by its German name of (Old Prussian: Instrāpils, lt, Įsrutis; pl, Wystruć) – is a town in the Kaliningrad Oblast of Russia, where it is the administrative center of Chernyakhovsky District. Located at the confluence of the Instruch and Angrapa rivers, which unite to become the Pregolya river below Chernyakhovsk, the town had a population in 2017 of 36,423. History Chernyakhovsk was founded in 1336 by the Teutonic Knights on the site of a former Old Prussian fortification when Dietrich von Altenburg, the Grand Master of the Teutonic Knights, built a castle called ''Insterburg'' following the Prussian Crusade. During the Teutonic Knights' Northern Crusades campaign against the Grand Duchy of Lithuania, the town was devastated in 1376. The castle had been rebuilt as the seat of a Procurator and a settlement also named ''Insterburg'' grew up to serve it. In 1454, Polish King Casimir IV Jagiellon incorpor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kostka Number
In mathematics, the Kostka number ''K''λμ (depending on two Partition (number theory), integer partitions λ and μ) is a non-negative integer that is equal to the number of semistandard Young tableaux of shape λ and weight μ. They were introduced by the mathematician Carl Kostka in his study of symmetric functions (). For example, if λ = (3, 2) and μ = (1, 1, 2, 1), the Kostka number ''K''λμ counts the number of ways to fill a left-aligned collection of boxes with 3 in the first row and 2 in the second row with 1 copy of the number 1, 1 copy of the number 2, 2 copies of the number 3 and 1 copy of the number 4 such that the entries increase along columns and do not decrease along rows. The three such tableaux are shown at right, and ''K''(3, 2) (1, 1, 2, 1) = 3. Examples and special cases For any partition λ, the Kostka number ''K''λλ is equal to 1: the unique way to fill the Young diagram of shape λ = (λ1, λ2, ..., λ''m'') with λ1 copies of 1, λ2 copies of 2, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kostka Polynomial
In mathematics, Kostka polynomials, named after the mathematician Carl Kostka, are families of polynomials that generalize the Kostka numbers. They are studied primarily in algebraic combinatorics and representation theory. The two-variable Kostka polynomials ''K''λμ(''q'', ''t'') are known by several names including Kostka–Foulkes polynomials, Macdonald–Kostka polynomials or ''q'',''t''-Kostka polynomials. Here the indices λ and μ are integer partitions and ''K''λμ(''q'', ''t'') is polynomial in the variables ''q'' and ''t''. Sometimes one considers single-variable versions of these polynomials that arise by setting ''q'' = 0, i.e., by considering the polynomial ''K''λμ(''t'') = ''K''λμ(0, ''t''). There are two slightly different versions of them, one called transformed Kostka polynomials. The one-variable specializations of the Kostka polynomials can be used to relate Hall-Littlewood polynomials ''P''μ to Schur polynomials ''s''λ: : s_\lambda(x_ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crelle's Journal
''Crelle's Journal'', or just ''Crelle'', is the common name for a mathematics journal, the ''Journal für die reine und angewandte Mathematik'' (in English: ''Journal for Pure and Applied Mathematics''). History The journal was founded by August Leopold Crelle (Berlin) in 1826 and edited by him until his death in 1855. It was one of the first major mathematical journals that was not a proceedings of an academy. It has published many notable papers, including works of Niels Henrik Abel, Georg Cantor, Gotthold Eisenstein, Carl Friedrich Gauss and Otto Hesse. It was edited by Carl Wilhelm Borchardt from 1856 to 1880, during which time it was known as ''Borchardt's Journal''. The current editor-in-chief is Rainer Weissauer (Ruprecht-Karls-Universität Heidelberg) Past editors * 1826–1856 August Leopold Crelle * 1856–1880 Carl Wilhelm Borchardt * 1881–1888 Leopold Kronecker, Karl Weierstrass * 1889–1892 Leopold Kronecker * 1892–1902 Lazarus Fuchs * 1903–1928 Kurt Hens ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
19th-century German Mathematicians
The 19th (nineteenth) century began on 1 January 1801 ( MDCCCI), and ended on 31 December 1900 ( MCM). The 19th century was the ninth century of the 2nd millennium. The 19th century was characterized by vast social upheaval. Slavery was abolished in much of Europe and the Americas. The First Industrial Revolution, though it began in the late 18th century, expanding beyond its British homeland for the first time during this century, particularly remaking the economies and societies of the Low Countries, the Rhineland, Northern Italy, and the Northeastern United States. A few decades later, the Second Industrial Revolution led to ever more massive urbanization and much higher levels of productivity, profit, and prosperity, a pattern that continued into the 20th century. The Islamic gunpowder empires fell into decline and European imperialism brought much of South Asia, Southeast Asia, and almost all of Africa under colonial rule. It was also marked by the collapse of the large S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1846 Births
Events January–March * January 5 – The United States House of Representatives votes to stop sharing the Oregon Country with the United Kingdom. * January 13 – The Milan–Venice railway's bridge, over the Venetian Lagoon between Mestre and Venice in Italy, opens, the world's longest since 1151. * February 4 – Many Mormons begin their migration west from Nauvoo, Illinois, to the Great Salt Lake, led by Brigham Young. * February 10 – First Anglo-Sikh War: Battle of Sobraon – British forces defeat the Sikhs. * February 18 – The Galician slaughter, a peasant revolt, begins. * February 19 – United States president James K. Polk's annexation of the Republic of Texas is finalized by Texas president Anson Jones in a formal ceremony of transfer of sovereignty. The newly formed Texas state government is officially installed in Austin. * February 20– 29 – Kraków uprising: Galician slaughter – Polish nationalists stage an uprising in the Free City ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1921 Deaths
Nineteen or 19 may refer to: * 19 (number), the natural number following 18 and preceding 20 * one of the years 19 BC, AD 19, 1919, 2019 Films * ''19'' (film), a 2001 Japanese film * ''Nineteen'' (film), a 1987 science fiction film Music * 19 (band), a Japanese pop music duo Albums * ''19'' (Adele album), 2008 * ''19'', a 2003 album by Alsou * ''19'', a 2006 album by Evan Yo * ''19'', a 2018 album by MHD * ''19'', one half of the double album ''63/19'' by Kool A.D. * ''Number Nineteen'', a 1971 album by American jazz pianist Mal Waldron * ''XIX'' (EP), a 2019 EP by 1the9 Songs * "19" (song), a 1985 song by British musician Paul Hardcastle. * "Nineteen", a song by Bad4Good from the 1992 album '' Refugee'' * "Nineteen", a song by Karma to Burn from the 2001 album ''Almost Heathen''. * "Nineteen" (song), a 2007 song by American singer Billy Ray Cyrus. * "Nineteen", a song by Tegan and Sara from the 2007 album '' The Con''. * "XIX" (song), a 2014 song by Slipknot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
People From Ełk
A person ( : people) is a being that has certain capacities or attributes such as reason, morality, consciousness or self-consciousness, and being a part of a culturally established form of social relations such as kinship, ownership of property, or legal responsibility. The defining features of personhood and, consequently, what makes a person count as a person, differ widely among cultures and contexts. In addition to the question of personhood, of what makes a being count as a person to begin with, there are further questions about personal identity and self: both about what makes any particular person that particular person instead of another, and about what makes a person at one time the same person as they were or will be at another time despite any intervening changes. The plural form "people" is often used to refer to an entire nation or ethnic group (as in "a people"), and this was the original meaning of the word; it subsequently acquired its use as a plural form of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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