Realizing additive monoids as mapping degree sets
arXiv:2607.27993
The paper proves that mapping degree sets are stable under multiplication by finite integer subsets containing 0 and under operations derived from additive submonoids of ℤ, and shows that any set constructed in this way can be realized as a mapping degree set, providing many infinite examples such as finite unions of arithmetic progressions starting at 0.
Abstract
We prove that mapping degree sets are stable under multiplication by finite subsets of containing and by sets obtained from additive submonoids of through finitely many sums and products. In particular, every set of the latter type occurs as a mapping degree set. As a consequence, we obtain a broad family of infinite mapping degree sets, including finite unions of arithmetic progressions starting at . These results extend previous work on the realization problem and are related to a question posed by Neofytidis, Wang, and Wang.
15 pages, no figures