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On k-hypertournament matrices

✍ Scribed by Youngmee Koh; Sangwook Ree

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
132 KB
Volume
373
Category
Article
ISSN
0024-3795

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✦ Synopsis

A k-hypertournament is a complete k-hypergraph with all k-edges endowed with orientations. The incidence matrix associated with a k-hypertournament is called a k-hypertournament matrix. Some properties of the hypertournament matrices are investigated. The sequences of the numbers of 1's and -1's of rows of a k-hypertournament matrix are respectively called the score sequence and the losing score sequence of the matrix and so of the corresponding hypertournament. A necessary and sufficient condition for a sequence to be the score (and losing score) sequence of a k-hypertournament is considered. We also find some conditions for the existence of k-hypertournament matrices with constant score sequence, called regular k-hypertournament matrices.

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## Abstract A hypertournament or a __k__‐tournament, on __n__ vertices, 2≀__k__≀__n__, is a pair __T__=(__V, E__), where the vertex set __V__ is a set of size __n__ and the edge set __E__ is the collection of all possible subsets of size __k__ of __V__, called the edges, each taken in one of its __