Results 21 to 30 of about 549,106 (324)

Simultaneous avoidance of generalized patterns

Ars Comb., 2002
In [BabStein] Babson and Steingr\'{\i}msson introduced generalized permutation patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation.
Kitaev, S., Mansour, T.
core   +5 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
openaire   +3 more sources

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
doaj   +1 more source

Pattern avoidance in flattened derangements [PDF]

Discrete Mathematics Letters
Toufik Mansour, Mark Shattuck
doaj   +2 more sources

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, Sergi Elizalde, Matthew B. Kennel   +2 more
doaj   +1 more source

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
openaire   +4 more sources

Pattern avoidance for alternating permutations and Young tableaux [PDF]

Journal of Combinatorial Theory - Series A, 2011
Joel Brewster Lewis
exaly   +2 more sources

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
openaire   +4 more sources

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, Zachary Hamaker, Justin M. Troyka   +2 more
openaire   +3 more sources

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
doaj   +1 more source