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The generating series of a walk in the quarter plane

Mak, Richard (2019) The generating series of a walk in the quarter plane. Master's Thesis / Essay, Mathematics.

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Abstract

We consider walks with short steps in the quarter plane, that is, walks starting at (0, 0) that take steps from a fixed subset of {(0, 1),(1, 1),(1, 0),(1, −1),(0, −1), (−1, −1),(−1, 0),(−1, 1)}. The walk being in the quarter plane means that no intermediate point has a negative coordinate. Combining previous works on this subject, we examine the problem of calculating the number of ways one can get from (0, 0) to (i, j) in k steps by examining the generating series associated to the walk. We apply existing theory to more quickly determine the size of a certain invariant of the walk called its group, by using the theory of elliptic surfaces. Many examples will illustrate the theory.

Item Type: Thesis (Master's Thesis / Essay)
Supervisor:
Supervisor nameSupervisor E mail
Top, J.J.Top@rug.nl
Degree programme: Mathematics
Thesis type: Master's Thesis / Essay
Language: English
Date Deposited: 15 Jul 2019
Last Modified: 16 Jul 2019 11:52
URI: http://fse.studenttheses.ub.rug.nl/id/eprint/20221

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