Results 11 to 20 of about 2,353,350 (290)
Pattern Avoidance in Partial Permutations [PDF]
The Electronic Journal of Combinatorics, 2011 Motivated by the concept of partial words, we introduce an analogous concept of partial permutations. A partial permutation of length $n$ with $k$ holes is a sequence of symbols $\pi=\pi_1\pi_2\dotsb\pi_n$ in which each of the symbols from the set $\{1,2,\dotsc,n-k\}$ appears exactly once, while the remaining $k$ symbols of $\pi$ are "holes".
Claesson, Anders +3 more
core +12 more sources
Discrete Mathematics, 2002 Using some properties and refinements of the Catalan numbers, the author gives a sequence of refinements on the enumeration of permutations avoiding patterns of length 3.
Linusson, Svante, Svante Linusson
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Pattern Avoidance Classes and Subpermutations [PDF]
The Electronic Journal of Combinatorics, 2005 Pattern avoidance classes of permutations that cannot be expressed as unions of proper subclasses can be described as the set of subpermutations of a single bijection. In the case that this bijection is a permutation of the natural numbers a structure theorem is given.
Mike D. Atkinson +2 more
core +7 more sources
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
doaj +6 more sources
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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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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On Pattern-Avoiding Partitions [PDF]
The Electronic Journal of Combinatorics, 2008 A set partition of size $n$ is a collection of disjoint blocks $B_1,B_2,\ldots$, $B_d$ whose union is the set $[n]=\{1,2,\ldots,n\}$. We choose the ordering of the blocks so that they satisfy $\min B_1 < \min B_2 < \cdots < \min B_d$. We represent such a set partition by a canonical sequence $\pi_1,\pi_2,\ldots,\pi_n$, with $\pi_i=j$ if $i\in ...
Vít Jelínek, Toufik Mansour
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On Pattern Avoidance in Matchings and Involutions [PDF]
The Electronic Journal of Combinatorics, 2022 We study the relationship between two notions of pattern avoidance for involutions in the symmetric group and their restriction to fixed-point-free involutions. The first is classical, while the second appears in the geometry of certain spherical varieties and generalizes the notion of pattern avoidance for perfect matchings studied by Jelínek.
Jonathan J. Fang +2 more
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Permutations Avoiding a Simsun Pattern [PDF]
The Electronic Journal of Combinatorics, 2020 A permutation $\pi$ avoids the simsun pattern $\tau$ if $\pi$ avoids the consecutive pattern $\tau$ and the same condition applies to the restriction of $\pi$ to any interval $[k].$ Permutations avoiding the simsun pattern $321$ are the usual simsun permutation introduced by Simion and Sundaram.
Barnabei, Marilena +3 more
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Grasshopper Avoidance of Patterns
The Electronic Journal of Combinatorics, 2016 Motivated by a geometrical Thue-type problem, we introduce a new variant of the classical pattern avoidance in words, where jumping over a letter in the pattern occurrence is allowed. We say that pattern $p\in E^+$ occurs with jumps in a word $w=a_1a_2\ldots a_k \in A^+$, if there exist a non-erasing morphism $f$ from $E^*$ to $A^*$ and a sequence ...
Michal Debski +2 more
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