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 super diagonal bargraphs, which can be naturally defined starting from skew Dyck paths.
Deustch, E., Munarini, E., Rinaldi, S. (2010). Skew Dyck paths, area, superdiagonal bargraphs. JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 140, 1550-1562.
Skew Dyck paths, area, superdiagonal bargraphs
RINALDI, SIMONE
2010-01-01
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 super diagonal bargraphs, which can be naturally defined starting from skew Dyck paths.
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https://hdl.handle.net/11365/10629
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