On a set-theoretic invariant
组合数学
2016-09-07 v3
摘要
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.
引用
@article{arxiv.math/0309318,
title = {On a set-theoretic invariant},
author = {Dion Gijswijt and Pieter Moree},
journal= {arXiv preprint arXiv:math/0309318},
year = {2016}
}
备注
5 pages, 1 table. Original title changed to `A combinatorial identity arising from cobordism theory'. Some typos corrected. To appear in Acta Math. Univ. Comenian (NS)