skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


  • Home
  • Search Results
  • Page 1 of 1

Search for: All records

Creators/Authors contains: "O’Neill, Christopher"

Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher. Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?

Some links on this page may take you to non-federal websites. Their policies may differ from this site.

  1. ; ; (, Bulletin of the Australian Mathematical Society)
    Abstract We continue our study of exponent semigroups of rational matrices. Our main result is that the matricial dimension of a numerical semigroup is at most its multiplicity (the least generator), greatly improving upon the previous upper bound (the conductor). For many numerical semigroups, including all symmetric numerical semigroups, our upper bound is tight. Our construction uses combinatorially structured matrices and is parametrised by Kunz coordinates, which are central to enumerative problems in the study of numerical semigroups. 
    more » « less
    Free, publicly-accessible full text available December 12, 2025
  2. ; ; ; ; (, Discrete Applied Mathematics)
    Full Text Available 
  3. ; ; ; (, Journal of the Australian Mathematical Society)
    Abstract For numerical semigroups with a specified list of (not necessarily minimal) generators, we describe the asymptotic distribution of factorization lengths with respect to an arbitrary modulus. In particular, we prove that the factorization lengths are equidistributed across all congruence classes that are not trivially ruled out by modular considerations. 
    more » « less
    Full Text Available 
  4. ; (, The American Mathematical Monthly)
    Full Text Available 
  5. ; ; ; ; ; ; (, Advances in Geometry)
    Abstract Several recent papers have examined a rational polyhedronPmwhose integer points are in bijection with the numerical semigroups (cofinite, additively closed subsets of the non-negative integers) containingm. A combinatorial description of the faces ofPmwas recently introduced, one that can be obtained from the divisibility posets of the numerical semigroups a given face contains. In this paper, we study the faces ofPmcontaining arithmetical numerical semigroups and those containing certain glued numerical semigroups, as an initial step towards better understanding the full face structure ofPm. In most cases, such faces only contain semigroups from these families, yielding a tight connection to the geometry ofPm. 
    more » « less
    Full Text Available 
  6. ; ; (, European Journal of Combinatorics)
    Full Text Available