dc.contributor.advisor | Ozaydin, Murad | |
dc.contributor.author | Edwards, Craig | |
dc.date.accessioned | 2019-05-10T13:11:39Z | |
dc.date.available | 2019-05-10T13:11:39Z | |
dc.date.issued | 2019-05-10 | |
dc.identifier.uri | https://hdl.handle.net/11244/319674 | |
dc.description.abstract | Even though the problem of counting points with integer coordinates on a (rational) polytope has connections to sophisticated mathematical topics like Algebraic K-Theory, Fourier-Dedekind Sums, Heegard-Floer Homology, Symplectic Geometry and more, the basic (open) problem(s) are easy to describe. For example the following has been an open problem for over 60 years: If a, b and c are coprime positive integers how many ways are there of obtaining a given natural number n as a sum of (nonnegative integer) multiples of a, b and c? The problem is giving an effective computable formula for this number f(n). We are able to find this formula for a particular case. Furthermore, we use a variety of techniques to find the secondary asymptotic in any case, along with an effective computable formula for the McNugget Monoid and a couple of infinite families. | en_US |
dc.language | en_US | en_US |
dc.subject | Combinatorics | en_US |
dc.title | THE ENUMERATION PROBLEM ON NUMERICAL MONOIDS | en_US |
dc.contributor.committeeMember | Schmidt, Ralf | |
dc.contributor.committeeMember | Forester, Max | |
dc.contributor.committeeMember | Martin, Kimball | |
dc.contributor.committeeMember | Havlicek, Joseph | |
dc.date.manuscript | 2019-05 | |
dc.thesis.degree | Ph.D. | en_US |
ou.group | College of Arts and Sciences::Department of Mathematics | en_US |