✦ LIBER ✦

Regular sets of matrices and applications

✍ Scribed by Jennifer Seberry; Xian-Mo Zhang

Publisher: Springer Japan
Year: 1993
Tongue: English
Weight: 469 KB
Volume: 9
Category: Article
ISSN: 0911-0119
DOI: 10.1007/bf02988305

No coin nor oath required. For personal study only.

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Machines whose main purpose is to permute and sort data are studied. The sets of permutations that can arise are analysed by means of ÿnite automata and avoided pattern techniques. Conditions are given for these sets to be enumerated by rational generating functions. As a consequence we give the ÿrs

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In this note we give an algebraic characterization of sets of uniqueness in terms of matrices with non-negative integer coefficients and prescribed row and column sums, and of the dominance order of partitions or majorization. Our proof uses some identities involving characters of the symmetric grou