Structure of long idempotent-sum free sequences over finite cyclic semigroups

2020/06/01 by Guoqing Wang, Wang, Guoqing
Computer Science · Mathematics · #semigroups and automata theory #Advanced Topology and Set Theory #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2006.00673

Abstract

Let S be a finite cyclic semigroup written additively. An element e of S is said to be idempotent if e+e=e. A sequence T over S is called \sl idempotent-sum free provided that no idempotent of S can be represented as a sum of one or more terms from T. We prove that an idempotent-sum free sequence over S of length over approximately a half of the size of S is well-structured. This result generalizes the Savchev-Chen Structure Theorem for zero-sum free sequences over finite cyclic groups.

Related

• Enumeration of idempotent-sum subsequences in finite cyclic semigroups and smooth sequences
• Structure of the largest idempotent-product free sequences in semigroups
• The subsums of zero-sum free sequences in finite cyclic groups
• Long zero-free sequences in finite cyclic groups
• Zero-sum-free sequences with few subsequence sums