Alternating subsets modulo m

Toufik Mansour, Augustine O. Munagi

Research output: Contribution to journalArticlepeer-review

Abstract

We enumerate increasing combinations of {1, 2, . . . , n} according to parity statistics defined on pairs of adjacent elements. Generating functions are used to devise a framework that addresses all questions on adjacencies of parities with respect to any modulus m > 1. In particular, we give a generalization of a classical result on alternating subsets which was previously known for the modulus 2. We also compute some generating functions for the number of combinations possessing special adjacent parity patterns.

Original languageEnglish
Pages (from-to)1313-1325
Number of pages13
JournalRocky Mountain Journal of Mathematics
Volume42
Issue number4
DOIs
StatePublished - 2012

Keywords

  • Alternating subset
  • Fibonacci number
  • Generating function
  • Parity statistic

ASJC Scopus subject areas

  • Mathematics (all)

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