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Your search keyword '"Primary 05B35, Secondary 94B05, 94B75"' showing total 2 results
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2 results on '"Primary 05B35, Secondary 94B05, 94B75"'

1. Tutte polynomial, complete invariant, and theta series

Author

Kume, Misaki, Miezaki, Tsuyoshi, Sakuma, Tadashi, and Shinohara, Hidehiro

Subjects
Mathematics - Combinatorics, Mathematics - Number Theory, Primary 05B35, Secondary 94B05, 94B75
Abstract

In this study, we present two results that relate Tutte polynomials. First, we provide new and complete polynomial invariants for graphs. We note that the number of variables of our polynomials is one. Second, let L_1 and L_2 be two non-isomorphic lattices. We state that L_1 and L_2 are theta series equivalent if those theta series are the same. The problem of identifying theta series equivalent lattices is discussed in Prof.~Conway's book The Sensual (Quadratic) Form with the title "Can You Hear the Shape of a Lattice?" In this study, we present a method to find theta series equivalent lattices using matroids and their Tutte polynomials., Comment: 13 pages, 1 figure

Published
2020

2. Tutte Polynomial, Complete Invariant, and Theta Series

Author

Misaki Kume, Hidehiro Shinohara, Tadashi Sakuma, and Tsuyoshi Miezaki

Subjects
Polynomial, Mathematics - Number Theory, Matroid, Primary 05B35, Secondary 94B05, 94B75, Theoretical Computer Science, Combinatorics, Quadratic equation, Lattice (order), FOS: Mathematics, Mathematics - Combinatorics, Discrete Mathematics and Combinatorics, Combinatorics (math.CO), Number Theory (math.NT), Invariant (mathematics), Tutte polynomial, Mathematics
Abstract

In this study, we present two results that relate Tutte polynomials. First, we provide new and complete polynomial invariants for graphs. We note that the number of variables of our polynomials is one. Second, let L_1 and L_2 be two non-isomorphic lattices. We state that L_1 and L_2 are theta series equivalent if those theta series are the same. The problem of identifying theta series equivalent lattices is discussed in Prof.~Conway's book The Sensual (Quadratic) Form with the title "Can You Hear the Shape of a Lattice?" In this study, we present a method to find theta series equivalent lattices using matroids and their Tutte polynomials., 13 pages, 1 figure

Published
2020
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