Mathematics and Physics Seminar Series
A Seminar Presentation
on Thursday
November 16, 2017
at 3:00 pm in
North Hall 102
at The University of New Haven
Characterizing gaps of numerical
Dr. Caleb Shor
Associate Professor
Department of Mathematics
Western New England University
Abstract: For G a set of positive integers with gcd(G) = 1, a numer-
ical semigroup S is the set of all non-negative linear combinations of
elements of G. One can show that there are finitely many positive in-
tegers, called gaps, that are not in S. As we will see, questions about
gaps have been posed in numerous contexts, including coins, stamps,
basketball, and chicken nuggets.
In this talk, we will explore a few problems related to numerical
semigroups and their gaps, including computation of the largest gap
(called the “Frobenius problem”), and the cardinality and sum of the
set of gaps. Additionally, we will see connections to the Bernoulli
numbers along with some current research questions.
Fur ther Information
For further information, please contact Dr. Yasanthi Kottegoda at the Department of Math-
ematics and Physics, Office: Maxcy 315, 203-932-1206,