Permutation statistics and linear extensions of posets
Journal of Combinatorial Theory Series A
An introduction to the analysis of algorithms
An introduction to the analysis of algorithms
Handbook of combinatorics (vol. 2)
Regular Article: Restricted 132-Avoiding Permutations
Advances in Applied Mathematics
Multi-avoidance of generalised patterns
Discrete Mathematics
Consecutive patterns in permutations
Advances in Applied Mathematics - Special issue on: Formal power series and algebraic combinatorics in memory of Rodica Simion, 1955-2000
Combinatorial Enumeration
The Art of Computer Programming, Volume 4, Fascicle 3: Generating All Combinations and Partitions
The Art of Computer Programming, Volume 4, Fascicle 3: Generating All Combinations and Partitions
Horse paths, restricted 132-avoiding permutations, continued fractions, and Chebyshev polynomials
Discrete Applied Mathematics
Segmental partially ordered generalized patterns
Theoretical Computer Science
Whole mirror duplication-random loss model and pattern avoiding permutations
Information Processing Letters
The joint distribution of consecutive patterns and descents in permutations avoiding 3-1-2
European Journal of Combinatorics
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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.