A self-similarity structure generated by king's walk
Let \(w(i,j)\) denote the number of lattice walks from \((0,0)\) to \((i,j)\) with steps \((0,1)\), \((1,0)\), and \((1,1)\). The paper studies this array of numbers modulo \(p\), where \(p\) is an odd prime. It is shown that \(w(i,j)\pmod p\) for \(0\leq i< p\) and \(0\leq j<p\) contains all information on this array. In particular, the pattern of zero entries is analyzed.
scientific article; zbMATH DE number 1743040
scientific article