A Combinatorial Theory of Higher-Dimensional Permutation Arrays
Source: Advances in Applied Mathematics, Volume 25, Number 2, August 2000 , pp. 194-211(18)
Publisher: Academic Press
Abstract:We define a class of hypercubic (shape [n]d) arrays that in a certain sense are d-dimensional analogs of permutation matrices with our motivation from algebraic geometry. Various characterizations of permutation arrays are proved, an efficient generation algorithm is given, and enumerative questions are discussed although not settled. There is a partial order on the permutation arrays, specializing to the Bruhat order on Sn when d equals 2, and specializing to the lattice of partitions of a d-set when n equals 2.
Document Type: Research Article
Publication date: August 1, 2000