Results 1 to 10 of about 90 (55)
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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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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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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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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On Chern classes of the tensor product of vector bundles
Acta Universitatis Sapientiae: Mathematica, 2022 We present two formulas for Chern classes (polynomial) of the tensor product of two vector bundles. In the first formula the Chern polynomial of the product is expressed as determinant of a polynomial in a matrix variable involving the Chern classes of ...
Szilágyi Zsolt
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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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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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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 For any branched double covering of compact Riemann surfaces, we consider the associated character varieties that are unitary in the global sense, which we call $\operatorname {\mathrm {GL}}_n\rtimes \!}$ -character varieties.
Cheng Shu
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