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All Journal Indonesian Journal of Combinatorics
Karaçam, Cemil
Department of Mathematics, Yıldız Technical University
Computer Science & IT Decision Sciences, Operations Research & Management

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4-Dimensional Lattice Path Enumeration with Arbitrary Steps Vural, Alper; Karaçam, Cemil
Indonesian Journal of Combinatorics Vol 7, No 2 (2023)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2023.7.2.1

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.
Co-Authors Vural, Alper