#### Date of Award

2015

#### Degree Name

Mathematics

#### College

College of Science

#### Type of Degree

M.A.

#### Document Type

Thesis

#### First Advisor

Elizabeth Niese

#### Second Advisor

John Drost

#### Third Advisor

Michael Schroeder

#### Abstract

An important problem in algebraic combinatorics is finding expansions of products of symmetric functions as sums of symmetric functions. Schur functions form a well-known basis for the ring of symmetric functions. The Littlewood-Richardson rule was introduced to expand the product of two Schur functions as a positive sum of Schur functions. Remmel and Whitney introduced an algorithmic way to find the coefficients of Schur functions appearing in the expansion. Haglund et al. introduced quasisymmetric Schur functions as a refinement of Schur functions. For quasisymmetric Schur functions, the Littlewood-Richardson rule was introduced to expand the product of a Schur and quasisymmetric Schur function as the positive sum of quasisymmetric Schur functions. We determine an algorithm similar to the Remmel-Whitney rule to find the coefficients of quasisymmetric Schur functions appearing in the expansion.

#### Subject(s)

Schur functions.

Algebraic functions.

Combinatorial analysis.

#### Recommended Citation

Anderson, Jennifer, "Multiplication Rules for Schur and Quasisymmetric Schur Functions" (2015). *Theses, Dissertations and Capstones*. 912.

https://mds.marshall.edu/etd/912