Combinatorial properties of lattice paths
Date
2017
Authors
Dube, Nolwazi Mitchel
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Abstract
We study a type of lattice path called a skew Dyck path which is a generalization of a Dyck path. Therefore we first introduce Dyck paths and study their enumeration according to various parameters such as number of peaks, valleys, doublerises and return steps. We study characteristics such as bijections with other combinatorial objects, involutions and statistics on skew Dyck paths. We then show enumerations of skew Dyck paths in relation to area, semi-base and semi-length. We finally introduce superdiagonal bargraphs which are associated with skew Dyck paths and enumerate them in relation to perimeter and area
Description
A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg in fulfillment of the requirements for the degree of Master of Science.Johannesburg, 30 May 2017.
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Citation
Dube, Nolwazi Mitchel (2017) Combinatorial properties of lattice paths, University of the Witwatersrand, Johannesburg, <http://hdl.handle.net/10539/23725>