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Introduction to partially ordered patterns

Kitaev, Sergey (2007) Introduction to partially ordered patterns. Discrete Applied Mathematics, 155 (8). pp. 929-944. ISSN 0166-218X

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Abstract

We review selected known results on partially ordered patterns (POPs) that include co-unimodal, multi- and shuffle patterns, peaks and valleys ((modified) maxima and minima) in permutations, the Horse permutations and others. We provide several new results on a class of POPs built on an arbitrary flat poset, obtaining, as corollaries, the bivariate generating function for the distribution of peaks (valleys) in permutations, links to Catalan, Narayana, and Pell numbers, as well as generalizations of a few results in the literature including the descent distribution. Moreover, we discuss a q-analogue for a result on non-overlapping segmented POPs. Finally, we suggest several open problems for further research.

Item type: Article
ID code: 49825
Keywords: non-overlapping occurrences of patterns, q-analogue, flat poset, co-unimodal pattern, bijection, generating function, Catalan numbers, Narayana numbers, Pell numbers, Electronic computers. Computer science, Discrete Mathematics and Combinatorics, Applied Mathematics
Subjects: Science > Mathematics > Electronic computers. Computer science
Department: Faculty of Science > Computer and Information Sciences
Depositing user: Pure Administrator
Date deposited: 15 Oct 2014 10:12
Last modified: 22 Mar 2017 13:34
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URI: https://strathprints.strath.ac.uk/id/eprint/49825
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