4-Dimensional Lattice Path Enumeration with Arbitrary Steps

Alper Vural, Cemil Karaçam

Abstract


Consider a set of vectors, L, which consists of vectors whose coordinates are 0 or 1. We find explicit formulas that counts the number of lattice paths from origin to (a,b,c,d) for using vectors in {(1,0,0,0),(0,1,0,0),(0,0,1,0),(0,0,0,1)} ∪ L for various choices of L. In some cases we also give the recursive formulas for the same problem. Next we determine the minimum number of vectors that must be used to reach (a,b,c,d), also called the minimum distance problem, for different sets of vectors.


Keywords


Lattice Path, Shortest Path, 4 Dimensions

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DOI: http://dx.doi.org/10.19184/ijc.2023.7.2.1

References

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ISSN: 2541-2205

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