Results 121 to 130 of about 181,403 (139)

On (Shape-)Wilf-Equivalence of Certain Sets of (Partially Ordered) Patterns [PDF]

Electronic Journal of Combinatorics
We prove a conjecture of Gao and Kitaev on Wilf-equivalence of sets of patterns $\{12345,12354\}$ and $\{45123,45213\}$ that extends the list of 10 related conjectures proved in the literature in a series of papers. To achieve our goals, we prove generalized versions of shape-Wilf-equivalence results of Backelin, West, and Xin and use a particular ...
Philip Biao Zhang, Alexander Burstein
exaly   +11 more sources

On Wilf Equivalence for Alternating Permutations [PDF]

Electronic Journal of Combinatorics, 2013
In this paper, we obtain several new classes of Wilf-equivalent patterns for alternating permutations. In particular, we prove that for any nonempty pattern $\tau$, the patterns $12\ldots k\oplus\tau$ and $k\ldots 21\oplus\tau$ are Wilf-equivalent for  alternating permutations, paralleling a result of Backelin, West, and Xin for Wilf equivalence for ...
Sherry H F Yan
exaly   +4 more sources

Refined Wilf-Equivalences by Comtet Statistics

Electronic Research Archive, 2021
39 pages, 2 tables, 2 figures.
Shishuo Fu, Zhicong Lin
exaly   +6 more sources

Wilf Equivalences Between Vincular Patterns in Inversion Sequences [PDF]

Applied Mathematics and Computation, 2021
18 pages, 9 ...
Sergi Elizalde
exaly   +5 more sources

Rook and Wilf Equivalence of Integer Partitions [PDF]

European Journal of Combinatorics, 2018
27, European Journal of Combinatorics ...
Jonathan Bloom
exaly   +5 more sources

Shape-Wilf-Equivalences for Vincular Patterns

Advances in Applied Mathematics, 2013
We extend the notion of shape-Wilf-equivalence to vincular patterns (also known as "generalized patterns" or "dashed patterns"). First we introduce a stronger equivalence on patterns which we call filling-shape-Wilf-equivalence. When vincular patterns $α$ and $β$ are filling-shape-Wilf-equivalent, we prove that the direct sum $α\oplusσ$ is filling ...
Andrew M Baxter
exaly   +4 more sources

A New Class of Wilf-Equivalent Permutations [PDF]

Journal of Algebraic Combinatorics, 2002
20 pages, 14 figures, corrected ...
Julian West
exaly   +4 more sources

A General Theory of Wilf-Equivalence for Catalan Structures [PDF]

Electronic Journal of Combinatorics, 2015
The existence of apparently coincidental equalities (also called Wilf-equivalences) between the enumeration sequences or generating functions of various hereditary classes of combinatorial structures has attracted significant interest. We investigate such coincidences among non-crossing matchings and a variety of other Catalan structures including Dyck
Michael H. Albert, Mathilde Bouvel
exaly   +5 more sources

Wilf Equivalence Relations for Consecutive Patterns [PDF]

Advances in Applied Mathematics, 2018
Two permutations $π$ and $τ$ are c-Wilf equivalent if, for each $n$, the number of permutations in $S_n$ avoiding $π$ as a consecutive pattern (i.e., in adjacent positions) is the same as the number of those avoiding $τ$. In addition, $π$ and $τ$ are strongly c-Wilf equivalent if, for each $n$ and $k$, the number of permutations in $S_n$ containing $k$
Sergi Elizalde
exaly   +4 more sources

A New Class of Multiset Wilf Equivalent Pairs

Discrete Mathematics, 2007
Let \(M\) be a multiset. A pair of patterns \((\sigma,\tau)\) is called multiset Wilf equivalent if, for any \(M\), the number of permutations of \(M\) that avoid \(\sigma\) is equal to the number of permutations of \(M\) that avoid \(\tau\). In this paper the author shows that if \(\sigma_{n-2}\) is a permutation of \(\{1^{x_1}, 2^{x_2},\dots, (n-2 ...
exaly   +4 more sources