Parity-alternating permutations and successions

Augustine Munagi 1
  • 1 School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits, 2050, Johannesburg, South Africa

Abstract

The study of parity-alternating permutations of {1, 2, … n} is extended to permutations containing a prescribed number of parity successions — adjacent pairs of elements of the same parity. Several enumeration formulae are computed for permutations containing a given number of parity successions, in conjunction with further parity and length restrictions. The objects are classified using direct construction and elementary combinatorial techniques. Analogous results are derived for circular permutations.

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