Results 1 to 10 of about 904 (36)

Skew characters and cyclic sieving

Forum of Mathematics, Sigma, 2021
In 2010, Rhoades proved that promotion on rectangular standard Young tableaux, together with the associated fake-degree polynomial, provides an instance of the cyclic sieving phenomenon.
Per Alexandersson, Stephan Pfannerer, Martin Rubey, Joakim Uhlin   +3 more
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A combinatorial model for the transition matrix between the Specht and $\operatorname {SL}_2$ -web bases

Forum of Mathematics, Sigma, 2023
We introduce a new class of permutations, called web permutations. Using these permutations, we provide a combinatorial interpretation for entries of the transition matrix between the Specht and $\operatorname {SL}_2$ -web bases of the irreducible
Byung-Hak Hwang, Jihyeug Jang, Jaeseong Oh   +2 more
doaj   +1 more source

A Topological View of Reed–Solomon Codes

Mathematics, 2021
We studied a particular class of well known error-correcting codes known as Reed–Solomon codes. We constructed RS codes as algebraic-geometric codes from the normal rational curve.
Alberto Besana, Cristina Martínez
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Convexity of tableau sets for type A Demazure characters (key polynomials), parabolic Catalan numbers [PDF]

Discrete Mathematics & Theoretical Computer Science, 2018
This is the first of three papers that develop structures which are counted by a "parabolic" generalization of Catalan numbers. Fix a subset R of {1,..,n-1}. Consider the ordered partitions of {1,..,n} whose block sizes are determined by R. These are the
Robert A. Proctor, Matthew J. Willis
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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
doaj   +1 more source

THE POLYTABLOID BASIS EXPANDS POSITIVELY INTO THE WEB BASIS

Forum of Mathematics, Sigma, 2019
We show that the transition matrix from the polytabloid basis to the web basis of the irreducible $\mathfrak{S}_{2n}$-representation of shape $(n,n)$ has nonnegative integer entries. This proves a conjecture of Russell and Tymoczko [Int. Math. Res. Not.,
BRENDON RHOADES
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DUAL EQUIVALENCE GRAPHS I: A NEW PARADIGM FOR SCHUR POSITIVITY

Forum of Mathematics, Sigma, 2015
We make a systematic study of a new combinatorial construction called a dual equivalence graph. We axiomatize these graphs and prove that their generating functions are symmetric and Schur positive.
SAMI H. ASSAF
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Increasing subsequences, matrix loci and Viennot shadows

Forum of Mathematics, Sigma
Let ${\mathbf {x}}_{n \times n}$ be an $n \times n$ matrix of variables, and let ${\mathbb {F}}[{\mathbf {x}}_{n \times n}]$ be the polynomial ring in these variables over a field ${\mathbb {F}}$ .
Brendon Rhoades
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Delta and Theta Operator Expansions

Forum of Mathematics, Sigma
We give an elementary symmetric function expansion for the expressions $M\Delta _{m_\gamma e_1}\Pi e_\lambda ^{\ast }$ and $M\Delta _{m_\gamma e_1}\Pi s_\lambda ^{\ast }$ when $t=1$ in terms of what we call $\gamma $ -parking ...
Alessandro Iraci, Marino Romero
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Δ–Springer varieties and Hall–Littlewood polynomials

Forum of Mathematics, Sigma
The $\Delta $ -Springer varieties are a generalization of Springer fibers introduced by Levinson, Woo and the author that have connections to the Delta Conjecture from algebraic combinatorics.
Sean T. Griffin
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