Zobrazeno 1 - 10
of 41
pro vyhledávání: '"Ranked poset"'
Akademický článek
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Autor:
Sam Hopkins, Colin Defant
For a Weyl group $W$ of rank $r$, the $W$-Catalan number is the number of antichains of the poset of positive roots, and the $W$-Narayana numbers refine the $W$-Catalan number by keeping track of the cardinalities of these antichains. The $W$-Narayan
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::50698540eb8dfab592c2fb11a457e34f
http://arxiv.org/abs/2101.02329
http://arxiv.org/abs/2101.02329
Autor:
Toshiaki Maeno, Yasuhide Numata
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, Vol DMTCS Proceedings vol. AR,..., Iss Proceedings (2012)
We introduce a certain class of algebras associated to matroids. We prove the Lefschetz property of the algebras for some special cases. Our result implies the Sperner property for the Boolean lattice and the vector space lattice.
Externí odkaz:
https://doaj.org/article/640e91106e7145c59c5e09572d5bb86e
Autor:
Tyler Kloefkorn
Publikováno v:
Journal of Algebra. 487:138-160
To a finite ranked poset Γ we associate a finite-dimensional graded quadratic algebra R Γ . Assuming Γ satisfies a combinatorial condition known as uniform, R Γ is related to a well-known algebra, the splitting algebra A Γ . First introduced by
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::7a4f059e017e5d3921314ff90a8a5bc7
https://doi.org/10.1016/j.jalgebra.2017.05.023
https://doi.org/10.1016/j.jalgebra.2017.05.023
Motivation coming from the study of affine Weyl groups, a structure of ranked poset is defined on the set of circular permutations in $S_n$ (that is, $n$-cycles). It is isomorphic to the poset of so-called admitted vectors, and to an interval in the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fe52bc9bb9b89f56e14cf351984e92ad
Akademický článek
Tento výsledek nelze pro nepřihlášené uživatele zobrazit.
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Publikováno v:
Advances in Mathematics. 371:107252
We introduce two new partial orders on the standard Young tableaux of a given partition shape, in analogy with the strong and weak Bruhat orders on permutations. Both posets are ranked by the major index statistic offset by a fixed shift. The existen
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6087b455721158385dc6a04a25c6ba74
https://doi.org/10.1016/j.aim.2020.107252
https://doi.org/10.1016/j.aim.2020.107252
Autor:
Brad Shelton, Tyler Kloefkorn
Publikováno v:
Journal of Algebra. 422:660-682
We study a finite dimensional quadratic graded algebra R Γ defined from a finite ranked poset Γ. This algebra has been central to the study of the splitting algebras A Γ introduced by Gelfand, Retakh, Serconek and Wilson [4] . Those algebras are k
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::24fd0804c01bb39adb24c5f15413f11a
https://doi.org/10.1016/j.jalgebra.2014.08.050
https://doi.org/10.1016/j.jalgebra.2014.08.050
Autor:
Kok Bin Wong, Cheng Yeaw Ku
Publikováno v:
Discrete Mathematics. 313:2239-2246
Let N be the set of positive integers, and let P ( n ) = ⋃ 1 ≤ l ≤ n { ( x 1 , … , x l ) ∈ N l : x 1 + ⋯ + x l = n } be the set of (ordered) partitions of n . We show that there exist a rank function and orderings ≤ c and ≺ such that
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::83adea8a0c52b49521f6ee766bc5727b
https://doi.org/10.1016/j.disc.2013.06.001
https://doi.org/10.1016/j.disc.2013.06.001
Autor:
Antony Mathews, Joseph Mathews, Sandi Klavžar, Narasimha-Shenoi Prasanth, Manoj Changat, Boštjan Brešar
Publikováno v:
Ars Mathematica Contemporanea. 2:27-33
The standard poset transit function of a poset P is a function T P that assigns to a pair of comparable elements the interval between them, while T P ( x , y ) = { x , y } for a pair x , y of incomparable elements. Posets in which the standard poset
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f022fd963d147ba2f44b7b13a7ca0fa9
https://doi.org/10.26493/1855-3974.72.9d1
https://doi.org/10.26493/1855-3974.72.9d1