Results 1 to 10 of about 122,748 (264)
Discrete Mathematics, 2022 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Suijie Wang, Zhousheng Mei
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Strict bounds for pattern avoidance [PDF]
Theoretical Computer Science, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
F Blanchet-Sadri
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Pattern Avoidance in Poset Permutations [PDF]
Order, 2015 We extend the concept of pattern avoidance in permutations on a totally ordered set to pattern avoidance in permutations on partially ordered sets. The number of permutations on $P$ that avoid the pattern $π$ is denoted $Av_P(π)$. We extend a proof of Simion and Schmidt to show that $Av_P(132) \leq Av_P(123)$ for any poset $P$, and we exactly classify ...
Sam Hopkins
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Patterns in matchings and rook placements [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 Extending the notion of pattern avoidance in permutations, we study matchings and set partitions whose arc diagram representation avoids a given configuration of three arcs.
Jonathan Bloom, Sergi Elizalde
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Pattern avoidance in “flattened” partitions
Discrete Mathematics, 2009 To flatten a set partition (with apologies to Mathematica) means to form a permutation by erasing the dividers between its blocks. Of course, the result depends on how the blocks are listed. For the usual listing--increasing entries in each block and blocks arranged in increasing order of their first entries--we count the partitions of [n] whose ...
David Callan
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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 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 E. Sagan
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