Bijections between directed animals, multisets and Grand-Dyck paths

Jean-Luc Baril, David Bevan, Sergey Kirgizov

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Abstract

An n-multiset of [k]={1,2,..., k} consists of a set of n elements from [k] where each element can be repeated. We present the bivariate generating function for n-multisets of [k] with no consecutive elements. For n=k, these multisets have the same enumeration as directed animals in the square lattice. Then we give constructive bijections between directed animals, multisets with no consecutive elements and Grand-Dyck paths avoiding the pattern DUD, and we show how classical and novel statistics are transported by these bijections.
Original languageEnglish
Article numberP2.10
Number of pages12
JournalThe Electronic Journal of Combinatorics
Volume27
Issue number2
DOIs
Publication statusPublished - 17 Apr 2020

Keywords

  • multisets
  • directed animals
  • Grand-Dyck paths
  • Motzkin
  • Catalan

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