Introduction to partially ordered patterns

Research output: Contribution to journalArticle

7 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)929-944
Number of pages16
JournalDiscrete Applied Mathematics
Volume155
Issue number8
Early online date27 Sep 2006
DOIs
Publication statusPublished - 15 Apr 2007

Keywords

  • non-overlapping occurrences of patterns
  • q-analogue
  • flat poset
  • co-unimodal pattern
  • bijection
  • generating function
  • Catalan numbers
  • Narayana numbers
  • Pell numbers

Fingerprint Dive into the research topics of 'Introduction to partially ordered patterns'. Together they form a unique fingerprint.

  • Cite this