Geodesic
Bijections between directed animals, multisets and Grand-Dyck paths
Jean-Luc Baril1 ; David Bevan ; Sergey Kirgizov
1LE2I, University of Burgundy, Dijon, France
The electronic journal of combinatorics, Tome 27 (2020) no. 2
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An $n$-multiset of $[k]=\{1,2,\ldots, k\}$ 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.
DOI : 10.37236/8826
Classification : 05A15, 05A19
Mots-clés : bivariate generating function

Jean-Luc Baril  1   ; David Bevan    ; Sergey Kirgizov 

1 LE2I, University of Burgundy, Dijon, France 
@article{10_37236_8826,
     author = {Jean-Luc Baril and David Bevan and Sergey Kirgizov},
     title = {Bijections between directed animals, multisets and {Grand-Dyck} paths},
     journal = {The electronic journal of combinatorics},
     year = {2020},
     volume = {27},
     number = {2},
     doi = {10.37236/8826},
     zbl = {1439.05013},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/8826/}
}
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Jean-Luc Baril; David Bevan; Sergey Kirgizov. Bijections between directed animals, multisets and Grand-Dyck paths. The electronic journal of combinatorics, Tome 27 (2020) no. 2. doi: 10.37236/8826

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