Results 121 to 130 of about 183,560 (141)

Shape-Wilf equivalence through length eight

We determine the shape-Wilf-equivalence classes of single permutation patterns at lengths seven and eight. The known Backelin-West-Xin and Stankova-West equivalences, with right direct-sum extension, generate 4,862 and 39,326 components, respectively, and the retained separation certificates distinguish all of them.
openaire   +1 more source

On Super-Strong Wilf Equivalence Classes of Permutations [PDF]

Electronic Journal of Combinatorics, 2018
Super-strong Wilf equivalence is a type of Wilf equivalence on words that was originally introduced as strong Wilf equivalence by Kitaev et al. [Electron. J. Combin. 16(2)] in $2009$. We provide a necessary and sufficient condition for two permutations in $n$ letters to be super-strongly Wilf equivalent, using distances between letters within a ...
Demetris Hadjiloucas, Ioannis Michos
exaly   +5 more sources

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

Refined Wilf-Equivalences by Comtet Statistics

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

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

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