Further enumeration results concerning a recent equivalence of restricted inversion sequences [PDF]
Discrete Mathematics & Theoretical Computer Science, 2022 Let asc and desc denote respectively the statistics recording the number of ascents or descents in a sequence having non-negative integer entries.
Toufik Mansour, Mark Shattuck
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A bijective proof of Kohnert's rule for Schubert polynomials [PDF]
, 2022 Kohnert proposed a formula for Schubert polynomials as the generating polynomial for certain unit cell diagrams obtained from the diagram of a permutation.
Assaf, Sami H.
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Enumeration of super-strong Wilf equivalence classes of permutations in the generalized factor order [PDF]
Discrete Mathematics & Theoretical Computer Science, 2019 Super-strong Wilf equivalence classes of the symmetric group ${\mathcal S}_n$ on $n$ letters, with respect to the generalized factor order, were shown by Hadjiloucas, Michos and Savvidou (2018) to be in bijection with pyramidal sequences of consecutive ...
Ioannis Michos, Christina Savvidou
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Inversion sequences avoiding 021 and another pattern of length four [PDF]
Discrete Mathematics & Theoretical Computer Science, 2023 We study the enumeration of inversion sequences that avoid the pattern 021 and another pattern of length four. We determine the generating trees for all possible pattern pairs and compute the corresponding generating functions.
Toufik Mansour, Gökhan Yıldırım
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No extremal square-free words over large alphabets [PDF]
, 2021 A word is square-free if it does not contain any square (a word of the form \(XX\)), and is extremal square-free if it cannot be extended to a new square-free word by inserting a single letter at any position.
Zhang, Shengtong +4 more
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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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Sensitivities and block sensitivities of elementary symmetric Boolean functions
Journal of Mathematical Cryptology, 2021 Boolean functions have important applications in molecular regulatory networks, engineering, cryptography, information technology, and computer science. Symmetric Boolean functions have received a lot of attention in several decades.
Zhang Jing, Li Yuan, Adeyeye John O.
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Restricted lonesum matrices [PDF]
, 2018 Lonesum matrices are matrices that are uniquely reconstructible from their row and column sum vectors. These matrices are enumerated by the poly-Bernoulli numbers; a sequence related to the multiple zeta values with a rich literature in number theory.
Bényi, Beáta, Beáta, Bényi
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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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Distribution of sets of descent tops and descent bottoms on restricted permutations [PDF]
Discrete Mathematics & Theoretical Computer ScienceIn this note, we prove some and conjecture other results regarding the distribution of descent top and descent bottom sets on some pattern-avoiding permutations.
Alexander Burstein
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