The Arithmetic Tutte Polynomials of the Classical Root Systems. (5th April 2014)

• Record Type: Journal Article
• Authors: Ardila, Federico; Castillo, Federico; Henley, Michael
• Is Part Of: International mathematics research notices. Volume 2015:Number 12(2015)
• Page Start: 3830
• Page End: 3877
• Publication Date: 2014-04-05
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/imrn/rnu050
• Languages: English
• ISSNs: 1073-7928

Abstract

Abstract: Many combinatorial and topological invariants of a hyperplane arrangement can be computed in terms of its Tutte polynomial. Similarly, many invariants of a toric arrangement can be computed in terms of its arithmetic Tutte polynomial. We compute the arithmetic Tutte polynomials of the classical root systems A n, B n, C n, and D n 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.