Results 1 to 10 of about 116,129 (149)
Pattern avoidance in parking functions [PDF]
Enumerative Combinatorics and Applications, 2023 In this paper, we view parking functions viewed as labeled Dyck paths in order to study a notion of pattern avoidance first introduced by Remmel and Qiu. In particular we enumerate the parking functions avoiding any set of two or more patterns of length 3, and we obtain a number of well-known combinatorial sequences as a result.
Ayomikun Adeniran, Lara Pudwell
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Avoidability of Palindrome Patterns [PDF]
The Electronic Journal of Combinatorics, 2021 We characterize the formulas that are avoided by every $\alpha$-free word for some $\alpha>1$. We show that the avoidable formulas whose fragments are of the form $XY$ or $XYX$ are $4$-avoidable. The largest avoidability index of an avoidable palindrome pattern is known to be at least $4$ and at most $16$. We make progress toward the conjecture that
Ochem, Pascal, Rosenfeld, Matthieu
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From Permutation Patterns to the Periodic Table [PDF]
ریاضی و جامعه, 2023 (The above abstract has been extracted by the translator from the original article (L. Pudwell, From Permutation Patterns to the Periodic Table, Notices of the American Mathematical Society, 67 994–1001.))Abstract: Permutation patterns is a burgeoning ...
Saeid Alikhani, Maryam Safazadeh
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Pattern-avoiding permutation powers [PDF]
Discrete Mathematics, 2020 Recently, B na and Smith defined strong pattern avoidance, saying that a permutation $ $ strongly avoids a pattern $ $ if $ $ and $ ^2$ both avoid $ $. They conjectured that for every positive integer $k$, there is a permutation in $S_{k^3}$ that strongly avoids $123\cdots (k+1)$.
Amanda Burcroff, Colin Defant
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Pattern Avoidance for Random Permutations [PDF]
Discrete Mathematics & Theoretical Computer Science, 2018 Using techniques from Poisson approximation, we prove explicit error bounds on the number of permutations that avoid any pattern. Most generally, we bound the total variation distance between the joint distribution of pattern occurrences and a ...
Harry Crane, Stephen DeSalvo
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Pattern avoidance in dynamical systems [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 Orbits generated by discrete-time dynamical systems have some interesting combinatorial properties. In this paper we address the existence of forbidden order patterns when the dynamics is generated by piecewise monotone maps on one-dimensional closed ...
José María Amigó +2 more
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Pattern-avoiding polytopes [PDF]
European Journal of Combinatorics, 2018 Two well-known polytopes whose vertices are indexed by permutations in the symmetric group $\mathfrak{S}_n$ are the permutohedron $P_n$ and the Birkhoff polytope $B_n$. We consider polytopes $P_n(Π)$ and $B_n(Π)$, whose vertices correspond to the permutations in $\mathfrak{S}_n$ avoiding a set of patterns $Π$. For various choices of $Π$, we explore the
Robert Davis, Bruce Sagan
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Matchings Avoiding Partial Patterns [PDF]
The Electronic Journal of Combinatorics, 2006 We show that matchings avoiding a certain partial pattern are counted by the $3$-Catalan numbers. We give a characterization of $12312$-avoiding matchings in terms of restrictions on the corresponding oscillating tableaux. We also find a bijection between matchings avoiding both patterns $12312$ and $121323$ and Schröder paths without peaks at level ...
Chen, William Y. C. +2 more
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Pattern Avoidance in Task-Precedence Posets [PDF]
Discrete Mathematics & Theoretical Computer Science, 2016 We have extended classical pattern avoidance to a new structure: multiple task-precedence posets whose Hasse diagrams have three levels, which we will call diamonds. The vertices of each diamond are assigned labels which are compatible with the poset.
Mitchell Paukner +3 more
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Large sets avoiding patterns [PDF]
Analysis & PDE, 2018 We construct subsets of Euclidean space of large Hausdorff dimension and full Minkowski dimension that do not contain nontrivial patterns described by the zero sets of functions. The results are of two types. Given a countable collection of $v$-variate vector-valued functions $f_q : (\mathbb{R}^{n})^v \to \mathbb{R}^m$ satisfying a mild regularity ...
Fraser, Robert, Pramanik, Malabika
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