2019/10/28 by Geroldinger, Alfred, Grynkiewicz, David J., Oh, Jun Seok +1 · 1 citation
#11B30 #11B50 #11B75 #20M13 #20M14 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1910.12484
Let G be a finite group. A sequence over G means a finite sequence of terms from G, where repetition is allowed and the order is disregarded. A product-one sequence is a sequence whose elements can be ordered such that their product equals the identity element of the group. The set of all product-one sequences over G (with concatenation of sequences as the operation) is a finitely generated C-monoid. Product-one sequences over dihedral groups have a variety of extremal properties. This article provides a detailed investigation, with methods from arithmetic combinatorics, of the arithmetic of the monoid of product-one sequences over dihedral groups.