The arithmetic Tutte polynomials of the classical root systems

2013/05/28 by Federico Ardila, Ardila, Federico, Federico Castillo +3
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.1305.6621

39 pages, 3 figures

arxiv created 2013/05/28 · arxiv updated 2013/05/30

Abstract

Many combinatorial and topological invariants of a hyperplane arrangement can be computed in terms of its Tutte polynomial. Similarly, many invariants of a hypertoric arrangement can be computed in terms of its arithmetic Tutte polynomial. We compute the arithmetic Tutte polynomials of the classical root systems of types A,B,C, and D, with respect to their integer, root, and weight lattices. We do it in two ways: by introducing a finite field method for arithmetic Tutte polynomials, and by enumerating signed graphs with respect to six parameters.

Related

• Tutte Polynomial of Ideal Arrangement
• Tutte polynomials of hyperplane arrangements and the finite field method
• Computing the Tutte polynomial of a hyperplane arrangement
• Tutte Polynomials of Symmetric Hyperplane Arrangements
• The Tutte Polynomial of Symmetric Hyperplane Arrangements