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
Presentation 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.
Recommended Citation
Krueger, Maxwell; Borchardt, Ashley; and Wren, Meghan, "Standard Set-Valued Young Tableaux and Product-Coproduct Prographs" (2017). Summer Interdisciplinary Research Symposium. 12.
https://scholar.valpo.edu/sires/12
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.