Rationality, irrationality, and Wilf equivalence in generalized factor order [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 Let $P$ be a partially ordered set and consider the free monoid $P^{\ast}$ of all words over $P$. If $w,w' \in P^{\ast}$ then $w'$ is a factor of $w$ if there are words $u,v$ with $w=uw'v$. Define generalized factor order on $P^{\ast}$ by letting $u \leq
Sergey Kitaev +3 more
doaj +6 more sources
Egge triples and unbalanced Wilf-equivalence [PDF]
, 2015 Egge conjectured that permutations avoiding the set of patterns $\{2143,3142,\tau\}$, where $\tau\in\{246135,254613,263514,524361,546132\}$, are enumerated by the large Schr\"oder numbers.
Bloom, Jonathan, Burstein, Alex
core +3 more sources
On a refinement of Wilf-equivalence for permutations [PDF]
The Electronic Journal of Combinatorics, 2014 Recently, Dokos et al. conjectured that for all $k, m\geq 1$, the patterns $ 12\ldots k(k+m+1)\ldots (k+2)(k+1) $ and $(m+1)(m+2)\ldots (k+m+1)m\ldots 21 $ are $maj$-Wilf-equivalent.
Ge, Huiyun +2 more
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Generating functions for Wilf equivalence under generalized factor order [PDF]
, 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 ...
Langley, Thomas +2 more
core +4 more sources
Decreasing subsequences in permutations and Wilf equivalence for involutions [PDF]
Journal of Algebraic Combinatorics, 2004 In a recent paper, Backelin, West and Xin describe a map $\phi ^*$ that recursively replaces all occurrences of the pattern $k... 21$ in a permutation $\sigma$ by occurrences of the pattern $(k-1)... 21 k$.
Bousquet-Melou, Mireille +1 more
core +4 more sources
Radiometric Constraints on the Timing, Tempo, and Effects of Large Igneous Province Emplacement
Geophysical Monograph Series, Page 27-82., 2021 Exploring the links between Large Igneous Provinces and dramatic environmental impact
An emerging consensus suggests that Large Igneous Provinces (LIPs) and Silicic LIPs (SLIPs) are a significant driver of dramatic global environmental and biological changes, including mass extinctions.
Jennifer Kasbohm +2 more
wiley +2 more sources
Bijections for generalized Wilf equivalences
Enumerative Combinatorics and ApplicationsStarting with an inclusion-exclusion proof of a combinatorial identity, a direct bijection can be produced using recursive subtraction (sometimes with a direct combinatorial description). We apply this method to identities for generalized Wilf equivalences among consecutive patterns in inversion sequences, giving direct bijective proofs of some ...
Melanie Ferreri
doaj +3 more sources
On (shape-)Wilf-equivalence for words [PDF]
Advances in Applied Mathematics, 2018 AmS-LaTeX, 13 pages; minor ...
Guo, Ting +2 more
openaire +3 more sources
On refinements of wilf-equivalence for involutions
Journal of Algebraic Combinatorics, 2023 Let $\mathcal{S}_n(π)$ (resp. $\mathcal{I}_n(π)$ and $\mathcal{AI}_n(π)$) denote the set of permutations (resp. involutions and alternating involutions) of length $n$ which avoid the permutation pattern $π$. For $k,m\geq 1$, Backelin-West-Xin proved that $|\mathcal{S}_n(12\cdots kτ)|= |\mathcal{S}_n(k\cdots 21τ)|$ by establishing a bijection between ...
Sherry H. F. Yan +2 more
openaire +2 more sources
Two examples of unbalanced Wilf-equivalence [PDF]
Journal of Combinatorics, 2015 10 pages, minor revision, to appear in Journal of ...
Burstein, Alexander, Pantone, Jay
openaire +2 more sources