𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A Combinatorial Theory of Higher-Dimensional Permutation Arrays

✍ Scribed by Kimmo Eriksson; Svante Linusson

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
153 KB
Volume
25
Category
Article
ISSN
0196-8858

No coin nor oath required. For personal study only.

✦ Synopsis

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.

πŸ“œ SIMILAR VOLUMES

Covering arrays of higher strength from
Covering arrays of higher strength from permutation vectors
✍ George B. Sherwood; Sosina S. Martirosyan; Charles J. Colbourn πŸ“‚ Article πŸ“… 2006 πŸ› John Wiley and Sons 🌐 English βš– 130 KB

## Abstract A __covering array__ __CA(N;t,k,v)__ is an __N × k__ array such that every __N × t__ sub‐array contains all __t__‐tuples from __v__ symbols __at least__ once, where __t__ is the __strength__ of the array. Covering arrays are used to generate software test suites to cover all __t__‐sets

A Decomposition of Fl(n)d Indexed by Per
A Decomposition of Fl(n)d Indexed by Permutation Arrays
✍ Kimmo Eriksson; Svante Linusson πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 137 KB

We study a decomposition of Fl n d-1 , where Fl n denotes the flag manifold over n . The strata are defined by the dimensions of intersections of one space from each flag, so for d equal to 2 this is the usual Bruhat cell decomposition. The strata are indexed by "permutation arrays," which are d-dim

Effective Field Theory Description of th
Effective Field Theory Description of the Higher Dimensional Quantum Hall Liquid
✍ Bogdan Andrei Bernevig; Chyh-Hong Chern; Jiang-Ping Hu; Nicolaos Toumbas; Shou-C πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 189 KB

We derive an effective topological field theory model of the four dimensional quantum Hall liquid state recently constructed by Zhang and Hu. Using a generalization of the flux attachment transformation, the effective field theory can be formulated as a U (1) Chern-Simons theory over the total confi

A combinatorial approach to transitive e
A combinatorial approach to transitive extensions of generously unitransitive permutation groups
✍ M. H. Klin; D. M. Mesner; A. J. Woldar πŸ“‚ Article πŸ“… 2010 πŸ› John Wiley and Sons 🌐 English βš– 230 KB

## Abstract Motivated by symmetric association schemes (which are known to approximate generously unitransitive group actions), we formulate combinatorial approximations to transitive extensions of generously unitransitive permutation groups. Specifically, the notions of compatible and coherent par