2018/02/24 by Wang, Guoqing
#Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1802.08791
Let S be a nonempty commutative semigroup written additively. An element e of S is said to be idempotent if e+e=e. The Erdős-Burgess constant of the semigroup S is defined as the smallest positive integer ℓ such that any S-valued sequence T of length ℓ contain a nonempty subsequence the sum of whose terms is an idempotent of S. We make a study of \rm I(S) when S is a direct product of arbitrarily many of cyclic semigroups. We give the necessary and sufficient conditions such that \rm I(S) is finite, and in particular, we obtain sharp bounds of \rm I(S) in case \rm I(S) is finite, and determine the precise values of \rm I(S) in some cases which unifies some well known results on the precise values of Davenport constant in the setting of commutative semigroups.