Results 11 to 20 of about 122,748 (264)
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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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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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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Consecutive patterns in permutations: clusters and generating functions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We use the cluster method in order to enumerate permutations avoiding consecutive patterns. We reprove and generalize in a unified way several known results and obtain new ones, including some patterns of length 4 and 5, as well as some infinite families
Sergi Elizalde, Marc Noy
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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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Pattern Avoidance in Ascent Sequences [PDF]
The Electronic Journal of Combinatorics, 2011 Ascent sequences are sequences of nonnegative integers with restrictions on the size of each letter, depending on the number of ascents preceding it in the sequence. Ascent sequences have recently been related to $(2+2)$-free posets and various other combinatorial structures.
Duncan, Paul, Steingrimsson, Einar
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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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Pattern Avoidance Over a Hypergraph [PDF]
The Electronic Journal of Combinatorics, 2021 A classic result of Marcus and Tardos (previously known as the Stanley-Wilf conjecture) bounds from above the number of $n$-permutations ($\sigma \in S_n$) that do not contain a specific sub-permutation. In particular, it states that for any fixed permutation $\pi$, the number of $n$-permutations that avoid $\pi$ is at most exponential in $n$.
Benjamin Gunby, Maxwell Fishelson
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On Pattern Avoiding Indecomposable Permutations [PDF]
Integers, 2016 Comtet introduced the notion of indecomposable permutations in 1972. A permutation is indecomposable if and only if it has no proper prefix which is itself a permutation. Indecomposable permutations were studied in the literature in various contexts.
Gao, Alice L. L. +2 more
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Pattern-avoiding permutation powers [PDF]
Discrete Mathematics, 2020 16 pages, 1 ...
Amanda Burcroff, Colin Defant
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