On the generating function for consecutively weighted permutations

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We show that the analytic continuation of the exponential generating function associated to consecutive weighted pattern enumeration of permutations only has poles and no essential singularities. The proof uses the connection between permutation enumeration and functional analysis, and as well as the Laurent expansion of the associated resolvent. As a consequence, we give a partial answer to a question of Elizalde and Noy: when is the multiplicative inverse of the exponential generating function for the number permutations avoiding a single pattern an entire function? Our work implies that it is enough to verify that this function has no zeros to conclude that the inverse function is entire.

Original languageEnglish
Pages (from-to)262-265
Number of pages4
JournalEuropean Journal of Combinatorics
StatePublished - Oct 2014

Bibliographical note

Funding Information:
The author is grateful to Margaret Readdy and the referees for their comments on an earlier version of this article. The author was partially supported by National Science Foundation grant DMS 0902063 .

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics


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