Title

Standard Set-Valued Young Tableaux and Product-Coproduct Prographs

Faculty Sponsor

Paul Drube

College

Arts and Sciences

Department/Program

VERUM

ORCID Identifier(s)

orcid.org/0000-0002-4012-4900; orcid.org/0000-0003-0074-3800; orcid.org/0000-0002-0173-2604

Document Type

Poster Presentation

Symposium Date

Summer 7-31-2017

Abstract

Standard set-valued Young tableaux are a generalization of standard Young tableaux where cells can contain more than one integer. Unlike standard Young tableaux, there is no known method to count the number of distinct set-valued tableaux of arbitrary shape. We construct bijections between standard set-valued tableaux and k-ary product-coproduct prographs, a generalization of k-ary trees, where internal vertices may be interpreted as either a k-ary product or k-ary coproduct. We present a bijection between 3-row rectangular tableaux that have k−1 integers in each middle row cell, and k-ary prographs with n products and coproducts, and then generalize our bijection to non-rectangular tableaux. We use this bijection to count the number of tableaux for small n. Furthermore, we investigate various intuitive operations on prographs and the corresponding tableaux. Finally, we define an analogue of the Schutzenberger involution for standard set-valued tableaux and show it corresponds to a 180-degree rotation on prographs.

Biographical Information about Author(s)

Ashley Borchardt majors in mathematics, mathematics education, and teaching English as a second language at Minnesota State University Moorhead. She is going into her final year of undergraduate studies. After graduation, she intends to teach secondary education for five years. Then, she intends to work toward her doctorate in mathematics.

Maxwell Krueger is a rising-senior at Muhlenberg College in Allentown, PA, where he studies mathematics and theatre. He fell in love with math in his senior year of high school. This love of math has grown during undergrad, and he plans to attend graduate school for math once he finishes.

Meghan Wren is entering her final year of undergrad at The College at Brockport, studying mathematics. She found her passion in math as a math and secondary education major and then decided to pursue a career in just math. She plans to attend graduate school in the fall of 2018.

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