Results 1 to 10 of about 337 (46)
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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A planar network proof for Hankel total positivity of type B Narayana polynomials [PDF]
Advances in Applied Mathematics, 2021 . The Hankel matrix of type B Narayana polynomials was proved to be totally positive by Wang and Zhu, and independently by Sokal. Pan and Zeng raised the problem of giving a planar network proof of this result.
Ethan Y. H. Li +3 more
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Flip-sort and combinatorial aspects of pop-stack sorting [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 Flip-sort is a natural sorting procedure which raises fascinating combinatorial questions. It finds its roots in the seminal work of Knuth on stack-based sorting algorithms and leads to many links with permutation patterns. We present several structural,
Andrei Asinowski +2 more
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Down-step statistics in generalized Dyck paths [PDF]
Discrete Mathematics & Theoretical Computer Science, 2022 The number of down-steps between pairs of up-steps in $k_t$-Dyck paths, a generalization of Dyck paths consisting of steps $\{(1, k), (1, -1)\}$ such that the path stays (weakly) above the line $y=-t$, is studied.
Andrei Asinowski +2 more
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Recent developments in combinatorial aspects of normal ordering
Enumerative Combinatorics and Applications, 2021 In this paper, we report on recent progress concerning combinatorial aspects of normal ordering. After giving a short introduction to the history and motivation of normal ordering, we present some recent developments.
M. Schork
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Patterns in Inversion Sequences I [PDF]
Discrete Mathematics & Theoretical Computer Science, 2016 Permutations that avoid given patterns have been studied in great depth for their connections to other fields of mathematics, computer science, and biology.
Sylvie Corteel +3 more
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Associated r-Dowling numbers and some relatives
, 2021 In this paper, we introduce a new generalization of Bell numbers, the s-associated r -Dowling numbers by combining two investigational directions. Here, r distinguished elements have to be in distinct blocks, some elements are coloured according to a ...
Eszter Gyimesi, Gábor Nyul
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The 26 Wilf-equivalence classes of length five quasi-consecutive patterns [PDF]
Discrete Mathematics & Theoretical Computer Science, 2018 We present two families of Wilf-equivalences for consecutive and quasi-consecutive vincular patterns. These give new proofs of the classification of consecutive patterns of length $4$ and $5$.
Evan Chen, Shyam Narayanan
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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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Continued fractions for permutation statistics [PDF]
Discrete Mathematics & Theoretical Computer Science, 2018 We explore a bijection between permutations and colored Motzkin paths that has been used in different forms by Foata and Zeilberger, Biane, and Corteel.
Sergi Elizalde
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