Mathematics – Combinatorics
Scientific paper
2006-03-05
Mathematics
Combinatorics
23 pages; Discrete Applied Mathematics, to appear
Scientific paper
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, Narayna, and Pell numbers, as well as generalizations of few results in the literature including the descent distribution. Moreover, we discuss q-analogue for a result on non-overlapping segmented POPs. Finally, we suggest several open problems for further research.
No associations
LandOfFree
Introduction to Partially Ordered Patterns does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Introduction to Partially Ordered Patterns, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Introduction to Partially Ordered Patterns will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-291993