Results 21 to 30 of about 183,560 (141)
Patterns in matchings and rook placements [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 Extending the notion of pattern avoidance in permutations, we study matchings and set partitions whose arc diagram representation avoids a given configuration of three arcs.
Jonathan Bloom, Sergi Elizalde
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Pattern-Avoidance in Binary Fillings of Grid Shapes (short version) [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 A $\textit{grid shape}$ is a set of boxes chosen from a square grid; any Young diagram is an example. This paper considers a notion of pattern-avoidance for $0-1$ fillings of grid shapes, which generalizes permutation pattern-avoidance.
Alexey Spiridonov
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Wilf Equivalences for Patterns in Rooted Labeled Forests [PDF]
, 2023 Building 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.
Ren, Michael
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Modified Growth Diagrams, Permutation Pivots, and the BWX Map $\phi^*$ [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 In their paper on Wilf-equivalence for singleton classes, Backelin, West, and Xin introduced a transformation $\phi^*$, defined by an iterative process and operating on (all) full rook placements on Ferrers boards. Bousquet-Mélou and Steingrimsson proved
Jonathan Bloom, Dan Saracino
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Wilf classification of triples of 4-letter patterns II [PDF]
Discrete Mathematics & Theoretical Computer Science, 2017 this is the second part of a complete paper in arXiv, see 1605 ...
David Callan +2 more
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Wilf-equivalence for singleton classes
Advances in Applied Mathematics, 2007 Given \(n\) and a permutation matrix \(M\) of rank less than \(n\), how many \(n \times n\) permutation matrices do \textit{not} have \(M\) as a submatrix? Letting \(S_n(M)\) be the set of \(n \times n\) permutation matrices not admitting \(M\) as a submatrix, we want \(| S_n(M)| \).
Jörgen Backelin, Julian West, Guoce Xin
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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
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Decreasing Subsequences in Permutations and Wilf Equivalence for Involutions [PDF]
Journal of Algebraic Combinatorics, 2005 In a recent paper, Backelin, West and Xin describe a map $ϕ^*$ that recursively replaces all occurrences of the pattern $k... 21$ in a permutation $σ$ by occurrences of the pattern $(k-1)... 21 k$. The resulting permutation $ϕ^*(σ)$ contains no decreasing subsequence of length $k$.
Bousquet-Mélou, Mireille +1 more
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Egge triples and unbalanced Wilf-equivalence
Australas. J Comb., 2014 Egge conjectured that permutations avoiding the set of patterns $\{2143,3142,τ\}$, where $τ\in\{246135,254613,263514,524361,546132\}$, are enumerated by the large Schröder numbers. Consequently, $\{2143,3142,τ\}$ with $τ$ as above is Wilf-equivalent to the set of patterns $\{2413,3142\}$. Burstein and Pantone proved the case of $τ=246135$. We prove the
Jonathan Bloom, Alexander Burstein
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Equivalences for pattern avoiding involutions and classification [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 We complete the Wilf classification of signed patterns of length 5 for both signed permutations and signed involutions. New general equivalences of patterns are given which prove Jaggard's conjectures concerning involutions in the symmetric group ...
Mark Dukes +3 more
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