Atoms of the relative block monoid

Baeth, Nicholas; Hoffmeier, Justin

doi:10.2140/involve.2009.2.29

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Atoms of the relative block monoid

Nicholas Baeth and Justin Hoffmeier

Vol. 2 (2009), No. 1, 29–36

DOI: 10.2140/involve.2009.2.29

Abstract

Let $G$ be a finite abelian group with subgroup $H$ and let $ℱ (G)$ denote the free abelian monoid with basis $G$ . The classical block monoid $ℬ (G)$ is the collection of sequences in $ℱ (G)$ whose elements sum to zero. The relative block monoid $ℬ_{H} (G)$ , defined by Halter-Koch, is the collection of all sequences in $ℱ (G)$ whose elements sum to an element in $H$ . We use a natural transfer homomorphism $θ : ℬ_{H} (G) \to ℬ (G ∕ H)$ to enumerate the irreducible elements of $ℬ_{H} (G)$ given an enumeration of the irreducible elements of $ℬ (G ∕ H)$ .

Keywords

zero-sum sequences, block monoids, finite abelian groups

Mathematical Subject Classification 2000

Primary: 11P70, 20M14

Milestones

Received: 15 September 2008

Revised: 10 November 2008

Accepted: 12 November 2008

Published: 18 March 2009

Communicated by Scott Chapman

Authors

Nicholas Baeth
Mathematics and Computer Science University of Central Missouri Warrensburg, MO 64093 United States

Justin Hoffmeier
Mathematics and Computer Science University of Central Missouri Warrensburg, MO 64093 United States

Vol. 2, No. 1, 2009