Results 31 to 40 of about 109 (102)
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 $ ^*$ that recursively replaces all occurrences of the pattern $k... 21$ in a permutation $ $ by occurrences of the pattern $(k-1)... 21 k$. The resulting permutation $ ^*( )$ contains no decreasing subsequence of length $k$.
Bousquet-Mélou, Mireille +1 more
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Rook and Wilf equivalence of integer partitions [PDF]
European Journal of Combinatorics, 2018 27, European Journal of Combinatorics ...
Jonathan Bloom, Dan Saracino
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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 \(| S_n(M)| \).
Backelin, Jörgen +2 more
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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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Wilf-Equivalence on $k$-ary Words, Compositions, and Parking Functions [PDF]
The Electronic Journal of Combinatorics, 2009 In this paper, we study pattern-avoidance in the set of words over the alphabet $[k]$. We say that a word $w\in[k]^n$ contains a pattern $\tau\in[\ell]^m$, if $w$ contains a subsequence order-isomorphic to $\tau$. This notion generalizes pattern-avoidance in permutations.
Jelínek, Vít, Mansour, Toufik
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Egge triples and unbalanced Wilf-equivalence
, 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
Bloom, Jonathan, Burstein, Alexander
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On Super-Strong Wilf Equivalence Classes of Permutations
The 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 ...
Hadjiloucas, Demetris +2 more
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Constraining strong c-Wilf equivalence using cluster poset asymptotics
Advances in Applied Mathematics, 2019 Let $π\in \mathfrak{S}_m$ and $σ\in \mathfrak{S}_n$ be permutations. An occurrence of $π$ in $σ$ as a consecutive pattern is a subsequence $σ_i σ_{i+1} \cdots σ_{i+m-1}$ of $σ$ with the same order relations as $π$. We say that patterns $π, τ\in \mathfrak{S}_m$ are strongly c-Wilf equivalent if for all $n$ and $k$, the number of permutations in ...
Lee, Mitchell, Sah, Ashwin
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Descents and des-Wilf equivalence of permutations avoiding certain nonclassical patterns [PDF]
Involve, a Journal of Mathematics, 2019 12 ...
Bielawa, Caden +3 more
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Using large language models to analyze political texts through natural language understanding
American Journal of Political Science, EarlyView.Abstract Large language models (LLMs) offer scalable alternatives to human experts when analyzing political texts for meaning, using natural language understanding (NLU). Qualitative NLU methods relying on human experts are severely limited by cost and scalability.
Kenneth Benoit +4 more
wiley +1 more source