Double Triangle Descendants of K5

Author: 
Date created: 
2017-12-05
Identifier: 
etd10502
Keywords: 
Phi^4-theory
C2-invariant
Double triangle reduction
K5-descendants
Zigzag graphs
Enumeration
Abstract: 

Feynman diagrams in phi^4 theory can be represented as 4-regular graphs. The Feynman integral, or even the Feynman period, is very hard to calculate. A graph invariant, called the c2-invariant, is conjecturally thought to be equal for two graphs when their periods are equal. Double triangle reduction of 4-regular graphs is known to preserve the c2-invariant. Double triangle descendants of K5 all have a c2-invariant that is a constant -1, and conjecturally, are the only graphs with this c2-invariant. This thesis studies the structure of K5-descendants to gain insight on the c2-invariant, get closer to solving the conjecture, and to study what is an interesting combinatorial operation in its own right. It will be shown that the minimum number of triangles in a descendant is 4. Closed-form generating functions are found for three families of K5-descendants. Two encodings, one for n-zigzags, and a general one for all K5-descendants, are found.

Document type: 
Thesis
Rights: 
This thesis may be printed or downloaded for non-commercial research and scholarly purposes. Copyright remains with the author.
File(s): 
Senior supervisor: 
Karen Yeats
Department: 
Science: Department of Mathematics
Thesis type: 
(Thesis) M.Sc.
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