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Abstract

In this paper we provide a bijection between all modular tableaux of size $kn$ and all partitions of $n$ labeled with $k$ colors. This bijection consists of a new function proven in this paper composed with mappings given by Garrett and Killpatrick in \cite{An1} and Stanton and White in \cite{An2}. We also demonstrate the novel construction and proof of a mapping essentially equivalent to Stanton and White's, but more useful for the purposes of the bijection mentioned above. By using the generating function for the number of $k$-colored partitions of $n$ in conjunction with our bijection, we can count the number of modular tableaux of size $kn$.

Author Bio

Nathan Meyer studies Mathematics and Political Science. After completing hisundergraduate studies he plans on attending law school. Partitions and tableaux arethe specific subfields that are his main mathematical focus while international lawremains his priority for Political Science. Outside of academics Nathan is also one ofthe Men's Ultimate Frisbee officers and part of Student Government on campus.

Daniel Mork majors in Mathematics, Psychology, and Norwegian. After receiving a Bachelor of Arts degree from St. Olaf College, he plans to undertake a multi-country bike ride through South America with friends from Alaska. Following a well-deserved break from academia, Dan has hopes to teach math for several years before possibly attending graduate school for a higher degree in psychology or electrical engineering. Outside of school he enjoys taking up new instruments, currently in the bluegrass genre, as well as other practical hobbies such as woodworking and baking.

Benjamin Simmons double majors in Mathematics and Physics. A passionate student of the liberal arts, Benjamin has also devoted significant study to French and the Western tradition of philosophy, theology, literature, and art. After graduation in 2012, he plans to pursue graduate studies in renewable energy technology engineering. In addition to academics, Benjamin enjoys singing in a choir, serving on the St. Olaf Honor Council, reading, and exploring the great outdoors.

Bjorn Wastvedt studies mostly Mathematics and Philosophy. After graduation from St. Olaf in 2012, he plans to begin graduate work in mathematics. Bjorn especially enjoys abstract algebra, combinatorics, and algorithms in the Mathematics and Computer Science departments at St. Olaf, while ethics and logic focus his Philosophy major. Alongside academics, he reads, spends time away from civilization, listens to classical music, and juggles torches.

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