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Generating and counting valid patterns in routes between two points

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Abstracts

Given two points on a plane, any rectilinear route between them can be specified by directions and lengths of constituent line segments. A word (pattern) over the alphabetN, E, S, andW is defined to represent a sequence of directions. The length of each line segment is ignored. In this paper we characterize and count all valid words, that is, those words representing non-selfcrossing routes.

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Abbreviations

V n :

The set of all valid words of lengthn.

P n :

The set of all words of lengthn.

References

  1. Liu, C.L.: Introduction to Combinatorial Mathematics. New York: McGraw-Hill 1968

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Asano, T. Generating and counting valid patterns in routes between two points. Graphs and Combinatorics 2, 9–13 (1986). https://doi.org/10.1007/BF01788071

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  • DOI: https://doi.org/10.1007/BF01788071

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