2019/06/27 by Jean-Luc Baril, Baril, Jean-Luc, David Bevan +3
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO
paper · pdf · doi:10.48550/arxiv.1906.11870
11 pages
arxiv created 2019/11/20 · arxiv updated 2019/11/21
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.