Combinatorial formulae for multiple set-valued labellings
We develope the geometric notions of general position maps, \(\pi\)- balanced and \(\pi\)-subbalanced sets and then apply them to prove two general combinatorial formulae for multiple set-valued labellings on simplices related to the celebrated Sperner combinatorial lemma [Abh. Math. Semin. Univ. Hamb. 6, 265-272 (1928; JFM 54.0614.01)]. We apply one of the combinatorial formulae to covering theory of simplices and obtain a new covering theorem which is a common generalization of the Shapley theorem and the Gale theorem.
scientific article; zbMATH DE number 537285