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Permutation Factorizations and Prime Parking Functions
Amarpreet Rattan
Department of Combinatorics and Optimization, University of Waterloo, Waterloo, ON, N2L 3G1, Canada
arattan@math.uwaterloo.ca
Annals of Combinatorics 10 (2) p. 237-254 June, 2006
AMS Subject Classification: 05A15, 05C05, 05E15
Abstract:
Permutation factorizations and parking functions have some parallel properties. Kim and Seo exploited these parallel properties to count the number of ordered, minimal factorizations of permutations of cycle type (n) and (1, n-1). In this paper, we use parking functions, new tree enumerations and other necessary tools, to extend the techniques of Kim and Seo to the cases (2, n-2) and (3, n-3).
Keywords: permutation factorizations, trees, parking functions

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