Results 21 to 30 of about 176,018 (136)
Two examples of unbalanced Wilf-equivalence [PDF]
Journal of Combinatorics, 2015 10 pages, minor revision, to appear in Journal of ...
Burstein, Alexander, Pantone, Jay
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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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On Wilf Equivalence for Alternating Permutations [PDF]
The 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 ...
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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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A General Theory of Wilf-Equivalence for Catalan Structures [PDF]
The 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
Albert Michael, Bouvel Mathilde
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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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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 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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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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