Results 1 to 10 of about 917 (68)
A Proof of the Extended Delta Conjecture
Forum of Mathematics, Pi, 2023 We prove the extended delta conjecture of Haglund, Remmel and Wilson, a combinatorial formula for $\Delta _{h_l}\Delta ' _{e_k} e_{n}$ , where $\Delta ' _{e_k}$ and $\Delta _{h_l}$ are Macdonald eigenoperators and $e_n$ is an ...
Jonah Blasiak +4 more
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A Symmetric Function of Increasing Forests
Forum of Mathematics, Sigma, 2021 For an indifference graph G, we define a symmetric function of increasing spanning forests of G. We prove that this symmetric function satisfies certain linear relations, which are also satisfied by the chromatic quasisymmetric function and unicellular $\
Alex Abreu, Antonio Nigro
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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 +3 more
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Row bounds needed to justifiably express flagged Schur functions with Gessel-Viennot determinants [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 Let $\lambda$ be a partition with no more than $n$ parts. Let $\beta$ be a weakly increasing $n$-tuple with entries from $\{ 1, ... , n \}$. The flagged Schur function in the variables $x_1, ...
Robert A. Proctor, Matthew J. Willis
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Askey-Wilson integral and its generalizations [PDF]
Advances in Differential Equations, 2014 We expand the Askey-Wilson (AW) density in a series of products of continuous q-Hermite polynomials times the density that makes these polynomials orthogonal.
P. Szabłowski
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A Shuffle Theorem for Paths Under Any Line
Forum of Mathematics, Pi, 2023 We generalize the shuffle theorem and its $(km,kn)$ version, as conjectured by Haglund et al. and Bergeron et al. and proven by Carlsson and Mellit, and Mellit, respectively. In our version the $(km,kn)$ Dyck paths on the combinatorial side
Jonah Blasiak +4 more
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Dunkl Operators for Complex Reflection Groups [PDF]
, 2001 Dunkl operators for complex reflection groups are defined in this paper. These commuting operators give rise to a parameterized family of deformations of the polynomial De Rham complex. This leads to the study of the polynomial ring as a module over the ‘
C. Dunkl, E. Opdam
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Journal of Inequalities and Applications, 2013 The judgement theorems of Schur geometric and Schur harmonic convexities for a class of symmetric functions are given. As their application, some analytic inequalities are established.MSC:26D15, 05E05, 26B25.
Huan-Nan Shi, Jing Zhang
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Forum of Mathematics, Sigma, 2023 Let G be a finite group. Let $H, K$ be subgroups of G and $H \backslash G / K$ the double coset space. If Q is a probability on G which is constant on conjugacy classes ( $Q(s^{-1} t s) = Q(t)$ ), then the random walk driven by Q on G ...
Persi Diaconis +2 more
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Schur-convexity of dual form of some symmetric functions
Journal of Inequalities and Applications, 2013 By the properties of a Schur-convex function, Schur-convexity of the dual form of some symmetric functions is simply proved.MSC:26D15, 05E05, 26B25.
Huan-Nan Shi, Jing Zhang
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