Journal of Integer Sequences, Vol. 21 (2018), Article 18.3.6

Enumerating Minimal Length Lattice Paths

Jackson Evoniuk, Steven Klee, and Van Magnan
Department of Mathematics
Seattle University
901 12th Avenue
Seattle, WA 98122


Given a finite set of integer vectors, S, we consider the set of all lattice walks comprised as ordered sequences of steps whose directions come from S. We further restrict our attention to walks of minimal length, meaning they cannot be shortened through some linear combination of allowable steps from S. We consider the problem of counting the number of such minimal walks terminating at a fixed point (a,b) for various choices of the set S.

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(Concerned with sequences A000108 A001006 A007318 A009766 A292435 A292436 A292437.)

Received December 9 2017; revised version received March 27 2018. Published in Journal of Integer Sequences, March 28 2018.

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