Results 1 to 10 of about 896 (74)
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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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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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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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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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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Does the group leader matter? The impact of monitoring activities and social ties of group leaders on the repayment performance of groupbased lending Eritrea [PDF]
, 2005 This paper analyzes whether the effects of monitoring and social ties of the group leader and other group members on repayment performance of groups differ, using data from an extensive questionnaire held in Eritrea among participants of 102 groups.
A Seltene +17 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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