#### Date of Submission

Spring 2019

#### Academic Programs and Concentrations

Mathematics

#### Project Advisor 1

Silvia Saccon

#### Abstract/Artist's Statement

A numerical monoid M generated by the natural numbers n_1, ..., n_k is a subset of {0, 1, 2, ...} whose elements are non-negative linear combinations of the generators n_1, ..., n_k. The set of factorizations of an element in M is the set of all the different ways to write that element as a linear combination of the generators. The length of a factorization of an element is the sum of the coefficients of that factorization. Since an element in a monoid can be written in different ways in terms of the generators, its set of factorization lengths may contain more than one element. In my project, I focus on the maximum factorization length of an element x in M, denoted by L(x), and the minimum factorization length of x, denoted by l(x), and I investigate for which numerical monoids M the conditions L(x+n_1)=L(x)+1 and l(x+n_k)=l(x)+1 hold for every element x in M.

#### Open Access Agreement

Open Access

#### Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

#### Recommended Citation

Schwartz, Maya Samantha, "Factorization Lengths in Numerical Monoids" (2019). *Senior Projects Spring 2019*. 245.

https://digitalcommons.bard.edu/senproj_s2019/245

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