Wong An elementary combinatorial analog of a theorem of

Abstract. Tucker’s Lemma is a combinatorial analog of the Borsuk-Ulam theorem and the case n = 2 was proposed by Tucker in 1945. Numerous generalizations and appli-cations of the Lemma have appeared since then. In 2006 Meunier proved the Lemma in its full generality in his Ph.D. thesis. There are generalizations and extensions of the Borsuk-Ulam theorem that do not yet have combinatorial analogs. In this note, we give a combinatorial analog of a result of Freeman J. Dyson and show that our result is equivalent to Dyson’s theorem. As with Tucker’s Lemma, we hope that this will lead to generaliza-tions and applications and ultimately a combinatorial analog of Yang’s theorem of which both Borsuk-Ulam and Dyson are special cases