Ballot Paths Avoiding Depth Zero Patterns

Details Ballot Paths Avoiding Depth Zero Patterns Ballot Paths Avoiding Depth Zero Patterns

2010-04-15

arxiv.org/abs/1004.2710v1

Journal OF Combinatorial Mathematics and Combinatorial Computing, August 2010

Mathematics

Combinatorics

12 pages, 23rd MCCCC

Scientific paper

In a paper by Sapounakis, Tasoulas, and Tsikouras \cite{stt}, the authors count the number of occurrences of patterns of length four in Dyck paths. In this paper we specify in one direction and generalize in another. We only count ballot paths that avoid a given pattern, where a ballot path stays weakly above the diagonal $y=x$, starts at the origin, and takes steps from the set $\{\uparrow ,\to \}=\{u,r\}$. A pattern is a finite string made from the same step set; it is also a path. Notice that a ballot path ending at a point along the diagonal is a Dyck path.

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