Results 1 to 10 of about 95 (94)
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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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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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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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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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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MacMahon’s statistics on higher-dimensional partitions
Forum of Mathematics, Sigma, 2023 We study some combinatorial properties of higher-dimensional partitions which generalize plane partitions. We present a natural bijection between d-dimensional partitions and d-dimensional arrays of nonnegative integers.
Alimzhan Amanov, Damir Yeliussizov
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Descent c-Wilf Equivalence [PDF]
Discrete Mathematics & Theoretical Computer Science, 2017 Let $S_n$ denote the symmetric group. For any $\sigma \in S_n$, we let $\mathrm{des}(\sigma)$ denote the number of descents of $\sigma$, $\mathrm{inv}(\sigma)$ denote the number of inversions of $\sigma$, and $\mathrm{LRmin}(\sigma)$ denote the number of
Quang T. Bach, Jeffrey B. Remmel
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Falling stars: a fall-decorated rational shuffle theorem
Forum of Mathematics, SigmaIn this paper, we formulate a rational analog of the fall Delta theorem and the Delta square conjecture. We find a new dinv statistic on fall-decorated paths on a (m+k)×(n+k) $(m+k) \times (n+k)$ left parenthesis m plus k right parenthesis times left
Alessandro Iraci +2 more
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