Results 31 to 40 of about 549,106 (324)
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
openaire +2 more sources
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
openaire +4 more sources
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
openaire +3 more sources
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
openaire +3 more sources
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
openaire +5 more sources
Pattern-avoiding permutation powers [PDF]
Discrete Mathematics, 2020 16 pages, 1 ...
Amanda Burcroff, Colin Defant
openaire +2 more sources
Deodhar Elements in Kazhdan-Lusztig Theory [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 The Kazhdan-Lusztig polynomials for finite Weyl groups arise in representation theory as well as the geometry of Schubert varieties. It was proved very soon after their introduction that they have nonnegative integer coefficients, but no simple all ...
Brant Jones
doaj +1 more source
Discrete Mathematics & Theoretical Computer Science, 2014 A general lattice theoretic construction of Reading constructs Hopf subalgebras of the Malvenuto-Reutenauer Hopf algebra (MR) of permutations. The products and coproducts of these Hopf subalgebras are defined extrinsically in terms of the embedding in MR.
Shirley Law
doaj +1 more source
Crucial abelian k-power-free words [PDF]
Discrete Mathematics & Theoretical Computer Science, 2010 Combinatorics
Amy Glen +2 more
doaj +1 more source
Wilf classification of triples of 4-letter patterns I [PDF]
Discrete Mathematics & Theoretical Computer Science, 2017 This paper is first part of a complete paper in arXiv , see 1605.04969.
David Callan +2 more
doaj +1 more source