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Washington State
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Combinatorics, Linear Algebra and Number Theory Seminar

Department of Mathematics and Statistics

WEBS 11

December 5, Monday, 4:10 - 5:00 PM

Matthew Hudelson

Department of Mathematics and Statistics

Washington State University

Combinatorics, Linear Algebra and Number Theory Seminar

Department of Mathematics and Statistics

WEBS 11

December 5, Monday, 4:10 - 5:00 PM

Matthew Hudelson

Department of Mathematics and Statistics

Washington State University

Title:
Tree Expressions and Graph Tilings

Abstract: We consider “tree expressions,” obtained as quotients of determinants of generalized Laplacian matrices of trees. For a specific example of the structures provided by tree expressions, this computation applied to paths yields a standard continued fraction structure.

As an application, we will examine how tree expressions arise in “graph tilings,” obtained by covering each edge of a graph together with zero, one, or two of its endpoints so that every vertex is accounted for exactly once in the tiling.

Abstract: We consider “tree expressions,” obtained as quotients of determinants of generalized Laplacian matrices of trees. For a specific example of the structures provided by tree expressions, this computation applied to paths yields a standard continued fraction structure.

As an application, we will examine how tree expressions arise in “graph tilings,” obtained by covering each edge of a graph together with zero, one, or two of its endpoints so that every vertex is accounted for exactly once in the tiling.