Results 61 to 70 of about 109 (102)
Consecutive pattern containment and c-Wilf equivalence
Advances in Applied MathematicsWe offer elementary proofs for several results in consecutive pattern containment that were previously demonstrated using ideas from cluster method and analytical combinatorics. Furthermore, we establish new general bounds on the growth rates of consecutive pattern avoidance in permutations.
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Generating functions for Wilf equivalence under generalized factor order
, 2010 Kitaev, Liese, Remmel, and Sagan recently defined generalized factor order on words comprised of letters from a partially ordered set $(P, \leq_P)$ by setting $u \leq_P w$ if there is a subword $v$ of $w$ of the same length as $u$ such that the $i$-th character of $v$ is greater than or equal to the $i$-th character of $u$ for all $i$. This subword $v$
Langley, Thomas, Liese, J., Remmel, J.
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Wilf equivalences for patterns in rooted labeled forests
Advances in Applied MathematicsBuilding off recent work of Garg and Peng, we continue the investigation into classical and consecutive pattern avoidance in rooted forests, resolving some of their conjectures and questions and proving generalizations whenever possible. Through extensions of the forest Simion-Schmidt bijection introduced by Anders and Archer, we demonstrate a new ...
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Wilf Equivalence for the Charge Statistic
, 2012 Savage and Sagan have recently defined a notion of st-Wilf equivalence for any permutation statistic st and any two sets of permutations $ $ and $ '$. In this paper we give a thorough investigation of st-Wilf equivalence for the charge statistic on permutations and use a bijection between the charge statistic and the major index to prove a conjecture
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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 ...
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Like-minded sources on Facebook are prevalent but not polarizing. [PDF]
Nature, 2023 Nyhan B +29 more
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An infinite family of inv-Wilf-equivalent permutation pairs
European Journal of Combinatorics, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Associations between critical consciousness and well-being in a national sample of college students during the COVID-19 pandemic. [PDF]
J Community Psychol, 2022 Maker Castro E +3 more
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On (Shape-)Wilf-Equivalence of Certain Sets of (Partially Ordered) Patterns
The Electronic Journal of CombinatoricsWe 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 ...
Burstein, Alexander +3 more
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On the combinatorics of crystal structures. II. Number of Wyckoff sequences of a given subdivision complexity. [PDF]
Acta Crystallogr A Found Adv, 2023 Hornfeck W, Červený K.
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