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Hits 1 – 4 of 4
1
Mahonian STAT on words
Kitaev, Sergey
;
Vajnovszki, Vincent
In: ISSN: 0020-0190 ; Information Processing Letters ; https://hal-univ-bourgogne.archives-ouvertes.fr/hal-01418254 ; Information Processing Letters, Elsevier, 2016, 116 (2), pp.157 - 162. ⟨10.1016/j.ipl.2015.09.006⟩ ; http://www.sciencedirect.com/science/article/pii/S0020019015001611 (2016)
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2
Avoiding vincular patterns on alternating words
Gao, Alice L.L.
;
Kitaev, Sergey
;
Zhang, Philip B.
. - 2016
Abstract:
A word $w=w_1w_2\cdots w_n$ is alternating if either $w_1
w_3
\cdots$ (when the word is up-down) or $w_1>w_2
w_4<\cdots$ (when the word is down-up). The study of alternating words avoiding classical permutation patterns was initiated by the authors in~\cite{GKZ}, where, in particular, it was shown that 123-avoiding up-down words of even length are counted by the Narayana numbers.However, not much was understood on the structure of 123-avoiding up-down words. In this paper, we fill in this gap by introducing the notion of a cut-pair that allows us to subdivide the set of words in question into equivalence classes. We provide a combinatorial argument to show that the number of equivalence classes is given by the Catalan numbers, which induces an alternative (combinatorial) proof of the corresponding result in~\cite{GKZ}.Further, we extend the enumerative results in~\cite{GKZ} to the case of alternating words avoiding a vincular pattern of length 3. We show that it is sufficient to enumerate up-down words of even length avoiding the consecutive pattern $\underline{132}$ and up-down words of odd length avoiding the consecutive pattern $\underline{312}$ to answer all of our enumerative questions. The former of the two key cases is enumerated by the Stirling numbers of the second kind.
URL:
https://strathprints.strath.ac.uk/55630/1/Gao_Kitaev_Zhang_DM2016_avoiding_vincular_patterns_on_alternating_words.pdf
https://strathprints.strath.ac.uk/55630/
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3
Mahonian STAT on words
Kitaev, Sergey
;
Vajnovszki, Vincent
. - 2016
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4
Word problem of the Perkins semigroup via directed acyclic graphs
Kitaev, Sergey
;
Seif, Steven
. - 2008
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