%% Papers Accepted
@article{fds221103,
Author = {C. O'Neill and R. Pelayo},
Title = {On the Linearity of OmegaPrimality in Numerical
Monoids},
Journal = {Journal of Pure and Applied Algebra},
Year = {2013},
url = {http://arxiv.org/abs/1309.7476},
Abstract = {In an atomic, cancellative, commutative monoid, the
omegavalue measures how far an element is from being prime.
In numerical monoids, we show that this invariant exhibits
eventual quasilinearity (i.e., periodic linearity). We apply
this result to describe the asymptotic behavior of the
omegafunction for a general numerical monoid and give an
explicit formula when the monoid has embedding dimension
2.},
Key = {fds221103}
}
%% Papers Submitted
@article{fds219347,
Author = {J. Haarmann and A. Kalauli and A. Moran and C. O'Neill and R.
Pelayo},
Title = {Factorization Properties of Leamer Monoids},
Journal = {Semigroup Forum},
Year = {2013},
url = {http://arxiv.org/abs/1309.7477},
Abstract = {The HunekeWiegand conjecture has prompted much recent
research in Commutative Algebra. In studying this conjecture
for certain classes of rings, GarciaSanchez and Leamer
construct a monoid S_Gamma^s whose elements correspond to
arithmetic sequences in a numerical monoid Gamma of step
size s. These monoids, which we call Leamer monoids, possess
a very interesting factorization theory that is
significantly different from the numerical monoids from
which they are derived. In this paper, we offer much of the
foundational theory of Leamer monoids, including an analysis
of their atomic structure, and investigate certain
factorization invariants. Furthermore, when S_Gamma^s is an
arithmetical Leamer monoid, we give an exact description of
its atoms and use this to provide explicit formulae for its
Delta set and catenary degree.},
Key = {fds219347}
}
