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28 March 2024
 
  » arxiv » math.CO/0309318

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On a set-theoretic invariant
Dion Gijswijt ; Pieter Moree ;
Date 19 Sep 2003
Subject Combinatorics MSC-class: 15A39; 11B99 | math.CO
AbstractLet a_1,...,a_m be positive real numbers. Besser and Moree considered weighted numbers of -1,+1 solutions of the linear inequality |a_i-a_j| < e_ka_k < a_i+a_j, with e_k=-1 of 1 and k running over the integers 1,...,m with i and j skipped. They introduced some invariants and near invariants related to this situation (invariant meaning here: not depending on the choice of i and j). The main result of their paper is extended here to a much more general setting, namely that of certain maps from finite sets to {-1,1}. Some applications are given.
Source arXiv, math.CO/0309318
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