A combinatorial theory of higher-dimensional permutation arrays
2000 (English)In: Advances in Applied Mathematics, ISSN 0196-8858, E-ISSN 1090-2074, Vol. 25, no 2, 194-211 p.Article in journal (Refereed) Published
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 S-n, when d equals 2, and specializing to the lattice of partitions of a d-set when n equals 2.
Place, publisher, year, edition, pages
2000. Vol. 25, no 2, 194-211 p.
permutations, high-dimensional, flags, intersections, Bruhat order, partition lattice
IdentifiersURN: urn:nbn:se:kth:diva-20017ISI: 000089174400003OAI: oai:DiVA.org:kth-20017DiVA: diva2:338710
QC 201005252010-08-102010-08-10Bibliographically approved