Results 71 to 80 of about 2,203 (125)
Classical pattern distributions in $\mathcal{S}_{n}(132)$ and $\mathcal{S}_{n}(123)$ [PDF]
Discrete Mathematics & Theoretical Computer Science, 2019 Classical pattern avoidance and occurrence are well studied in the symmetric group $\mathcal{S}_{n}$. In this paper, we provide explicit recurrence relations to the generating functions counting the number of classical pattern occurrence in the set of ...
Dun Qiu, Jeffrey Remmel
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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
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Consecutive Patterns in Inversion Sequences [PDF]
Discrete Mathematics & Theoretical Computer Science, 2019 An inversion sequence of length $n$ is an integer sequence $e=e_{1}e_{2}\dots e_{n}$ such that $0\leq e_{i}
Juan S. Auli, Sergi Elizalde
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Some results for Apostol-type polynomials associated with umbral algebra
, 2013 A family of the Apostol-type polynomials was introduced and investigated recently by Luo and Srivastava (see (Appl. Math. Comput. 217:5702-5728, 2011)). In this paper, we study this polynomial family on P, the algebra of polynomials in a single variable ...
Da-qian Lu, C. Xiang, Qiu-Ming Luo
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A Note on the generating function of p-Bernoulli numbers
, 2018 We use analytic combinatorics to give a direct proof of the closed formula for the generating function of $p$-Bernoulli numbers.Comment: 6 ...
Kuba, Markus
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Further results on enumeration of perfect matchings of Cartesian product graphs
Open MathematicsCounting perfect matchings is an interesting and challenging combinatorial task. It has important applications in statistical physics and chemistry. As the general problem is #P-complete, it is usually tackled by randomized heuristics and approximation ...
Wu Tingzeng, Zeng Xiaolin
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Zeros distribution and interlacing property for certain polynomial sequences
Open MathematicsIn this article, we first prove that the Hankel determinant of order three of the polynomial sequence {Pn(x)=∑k≥0P(n,k)xk}n≥0{\left\{{P}_{n}\left(x)={\sum }_{k\ge 0}P\left(n,k){x}^{k}\right\}}_{n\ge 0} is weakly (Hurwitz) stable, where P(n,k)P\left(n,k ...
Guo Wan-Ming
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Two-sided permutation statistics via symmetric functions
Forum of Mathematics, SigmaGiven a permutation statistic $\operatorname {\mathrm {st}}$ , define its inverse statistic $\operatorname {\mathrm {ist}}$ by . We give a general approach, based on the theory of symmetric functions, for finding the joint distribution of
Ira M. Gessel, Yan Zhuang
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On the critical exponents of generalized ballot sequences in three dimensions and large tandem walks. [PDF]
Aequ Math, 2022 Wallner M.
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