Skew Dyck paths |
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Authors: | Emeric Deutsch Emanuele Munarini Simone Rinaldi |
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Affiliation: | 1. Polytechnic University, Six Metrotech Center, Brooklyn, NY 11201, USA;2. Politecnico di Milano, Dipartimento di Matematica, Piazza Leonardo da Vinci 32, 20133 Milano, Italy;3. Università di Siena, Dipartimento di Matematica, pian dei Mantellini 44, 53100 Siena, Italy |
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Abstract: | In this paper we study the class S of skew Dyck paths, i.e. of those lattice paths that are in the first quadrant, begin at the origin, end on the x-axis, consist of up steps U=(1,1), down steps D=(1,-1), and left steps L=(−1,-1), and such that up steps never overlap with left steps. In particular, we show that these paths are equinumerous with several other combinatorial objects, we describe some involutions on this class, and finally we consider several statistics on S. |
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Keywords: | Lattice path Dyck path Motzkin path Hex tree Enumeration Bijection |
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