Aubrey Blecher ; Charlotte Brennan ; Arnold Knopfmacher - Descents after maxima in compositions

dmtcs:1251 - Discrete Mathematics & Theoretical Computer Science, March 1, 2014, Vol. 16 no. 1 -
Descents after maxima in compositions

Authors: Aubrey Blecher ORCID-iD1; Charlotte Brennan 1; Arnold Knopfmacher ORCID-iD1

  • 1 The John Knopfmacher Centre for Applicable Analysis and Number Theory [Johannesburg]

We consider compositions of n, i.e., sequences of positive integers (or parts) (σi)i=1k where σ1+σ2+...+σk=n. We define a maximum to be any part which is not less than any other part. The variable of interest is the size of the descent immediately following the first and the last maximum. Using generating functions and Mellin transforms, we obtain asymptotic expressions for the average size of these descents. Finally, we show with the use of a simple bijection between the compositions of n for n>1, that on average the descent after the last maximum is greater than the descent after the first.

Volume: Vol. 16 no. 1
Section: Combinatorics
Published on: March 1, 2014
Accepted on: July 23, 2015
Submitted on: May 21, 2013
Keywords: Discrete Mathematics,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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