Parabolic Catalan numbers count flagged Schur functions and their appearances as type A Demazure characters (key polynomials) [PDF]
Discrete Mathematics & Theoretical Computer Science, 2017 Fix an integer partition lambda that has no more than n parts. Let beta be a weakly increasing n-tuple with entries from {1,..,n}. The flagged Schur function indexed by lambda and beta is a polynomial generating function in x_1, .., x_n for certain ...
Robert A. Proctor, Matthew J. Willis
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FRIEZE PATTERNS WITH COEFFICIENTS
Forum of Mathematics, Sigma, 2020 Frieze patterns, as introduced by Coxeter in the 1970s, are closely related to cluster algebras without coefficients. A suitable generalization of frieze patterns, linked to cluster algebras with coefficients, has only briefly appeared in an unpublished ...
MICHAEL CUNTZ +2 more
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On applications of bipartite graph associated with algebraic structures
Open Mathematics, 2020 The latest developments in algebra and graph theory allow us to ask a natural question, what is the application in real world of this graph associated with some mathematical system? Groups can be used to construct new non-associative algebraic structures,
Zhang Xiujun +3 more
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A combinatorial realization of Schur-Weyl duality via crystal graphs and dual equivalence graphs [PDF]
, 2008 For any polynomial representation of the special linear group, the nodes of the corresponding crystal may be indexed by semi-standard Young tableaux. Under certain conditions, the standard Young tableaux occur, and do so with weight 0.
Assaf, Sami
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Zero-sum subsets of decomposable sets in Abelian groups [PDF]
, 2019 A subset $D$ of an Abelian group is $decomposable$ if $\emptyset\ne D\subset D+D$. In the paper we give partial answer to an open problem asking whether every finite decomposable subset $D$ of an Abelian group contains a non-empty subset $Z\subset D ...
Banakh, Taras, Ravsky, Alex
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EQUIVARIANT $K$ -THEORY OF GRASSMANNIANS
Forum of Mathematics, Pi, 2017 We address a unification of the Schubert calculus problems solved by Buch [A Littlewood–Richardson rule for the $K$ -theory of Grassmannians, Acta Math. 189 (
OLIVER PECHENIK, ALEXANDER YONG
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Krein-space operators determined by free product algebras induced by primes and graphs
Special Matrices, 2017 In this paper, we introduce certain Krein-space operators induced by free product algebras induced by both primes and directed graphs. We study operator-theoretic properties of such operators by computing free-probabilistic data containing number ...
Cho Ilwoo, Jorgensen Palle E. T.
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An inequality of Kostka numbers and Galois groups of Schubert problems [PDF]
, 2012 We show that the Galois group of any Schubert problem involving lines in projective space contains the alternating group. Using a criterion of Vakil and a special position argument due to Schubert, this follows from a particular inequality among Kostka ...
Brooks, Christopher J. +2 more
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Matrices induced by arithmetic functions acting on certain Krein spaces
Special Matrices, 2017 In this paper, we study matrices induced by arithmetic functions under certain Krein-space representations induced by (multi-)primes less than or equal to fixed positive real numbers.
Cho Ilwoo
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Matrices induced by arithmetic functions, primes and groupoid actions of directed graphs
Special Matrices, 2015 In this paper, we study groupoid actions acting on arithmetic functions. In particular, we are interested in the cases where groupoids are generated by directed graphs. By defining an injective map α from the graph groupoid G of a directed graph G to the
Cho Ilwoo, Jorgensen Palle E. T.
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