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 language | English |
---|---|
Article number | P2.10 |
Number of pages | 12 |
Journal | The Electronic Journal of Combinatorics |
Volume | 27 |
Issue number | 2 |
DOIs | |
Publication status | Published - 17 Apr 2020 |
Keywords
- multisets
- directed animals
- Grand-Dyck paths
- Motzkin
- Catalan