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Washington State
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Combinatorics, Linear Algebra and Number Theory Seminar

Department of Mathematics and Statistics

WEBS 11

August 29, Monday, 4:10 - 5:00 PM

Daryl DeFord

Department of Mathematics and Statistics

Washington State University

Combinatorics, Linear Algebra and Number Theory Seminar

Department of Mathematics and Statistics

WEBS 11

August 29, Monday, 4:10 - 5:00 PM

Daryl DeFord

Department of Mathematics and Statistics

Washington State University

Title: Enumeration Problems on Matched Product
Graphs

Abstract: Multiplex networks have become an important tool for studying complex and detailed social data. While from a mathematical perspective, this data can be summarized by edge-colored graphs, that model is insufficient for efficiently studying dynamics in social systems. In this talk I will introduce the matched product for graphs, which represents several standard multiplex constructions while also containing the previously studied Cartesian, rooted, and hierarchical products as special cases. An interesting feature of this new product is that it requires labellings of the individual component graphs, leading to natural combinatorial questions by considering permutations of the labels. As examples of these problems, I will present enumerative results about Stirling numbers of the first kind on these products and prove that the number of planar labelled matched products of paths is equal to the number of square consecutive-minima polygon permutations.

Abstract: Multiplex networks have become an important tool for studying complex and detailed social data. While from a mathematical perspective, this data can be summarized by edge-colored graphs, that model is insufficient for efficiently studying dynamics in social systems. In this talk I will introduce the matched product for graphs, which represents several standard multiplex constructions while also containing the previously studied Cartesian, rooted, and hierarchical products as special cases. An interesting feature of this new product is that it requires labellings of the individual component graphs, leading to natural combinatorial questions by considering permutations of the labels. As examples of these problems, I will present enumerative results about Stirling numbers of the first kind on these products and prove that the number of planar labelled matched products of paths is equal to the number of square consecutive-minima polygon permutations.