Note: The q-exponential generating function for permutations by consecutive patterns and inversions

Authors:
Don Rawlings
Affiliations:
Mathematics Department, California Polytechnic State University, San Luis Obispo, CA 93407, USA
Venue:
Journal of Combinatorial Theory Series A
Year:
2007

Citing 4
Cited 1

Enumerative combinatorics

Enumerative combinatorics
Review: Adjacencies in Words

Advances in Applied 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

Combinatorial Enumeration

The joint distribution of consecutive patterns and descents in permutations avoiding 3-1-2

European Journal of Combinatorics

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Abstract

The inverse of Fedou's insertion-shift bijection is used to deduce a general form for the q-exponential generating function for permutations by consecutive patterns (overlaps allowed) and inversion number from a result due to Jackson and Goulden for enumerating words by distinguished factors. Explicit q-exponential generating functions are then derived for permutations by the consecutive patterns 12...m, 12...(m-2)m(m-1), 1m(m-1)...2, and by the pair of consecutive patterns (123,132).