Position Vectors of Numerical Semigroups

Autor:	James Hamblin, Lance Bryant
Rok vydání:	2014
Předmět:	Discrete mathematics Pure mathematics Algebra and Number Theory Mathematics - Commutative Algebra Commutative Algebra (math.AC) Apéry's constant Set (abstract data type) Position (vector) Numerical semigroup FOS: Mathematics Enumeration Tuple Algebra over a field Mathematics
Zdroj:	Semigroup Forum. 91:28-38
ISSN:	1432-2137 0037-1912
DOI:	10.1007/s00233-014-9620-1
Popis:	We provide a new way to represent numerical semigroups by showing that the position of every Ap\'ery set of a numerical semigroup $S$ in the enumeration of the elements of $S$ is unique, and that $S$ can be re-constructed from this "position vector." We extend the discussion to more general objects called numerical sets, and show that there is a one-to-one correspondence between $m$-tuples of positive integers and the position vectors of numerical sets closed under addition by $m+1$. We consider the problem of determining which position vectors correspond to numerical semigroups. Comment: 10 pages, changed some terminology, removed last two sections to streamline article
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::60fde36c1558d38d10deee0b3a4c2672 https://doi.org/10.1007/s00233-014-9620-1 Zobrazit plný text záznamu Full text from SpringerLink