Skew Dyck paths,area, and superdiagonal bargraphs |
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Authors: | Emeric Deutsch Emanuele Munarini Simone Rinaldi |
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Institution: | 1. Polytechnic Institute of New York University, 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, via del Capitano 15, 53100 Siena, Italy |
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Abstract: | Skew Dyck paths are a generalization of ordinary Dyck paths, defined as paths using up steps U=(1,1), down steps D=(1,-1), and left steps L=(−1,-1), starting and ending on the x-axis, never going below it, and so that up and left steps never overlap. In this paper we study the class of these paths according to their area, extending several results holding for Dyck paths. Then we study the class of superdiagonal bargraphs, which can be naturally defined starting from skew Dyck paths. |
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Keywords: | Dyck paths enumeration Bargraphs Enumerative combinatorics |
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