On a set-theoretic invariant

Details On a set-theoretic invariant On a set-theoretic invariant

2003-09-19

arxiv.org/abs/math/0309318v3

Acta Math. Univ. Comenianae 74, 2(2005), 199-203

Mathematics

Combinatorics

5 pages, 1 table. Original title changed to `A combinatorial identity arising from cobordism theory'. Some typos corrected. To

Scientific paper

Let 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.

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