The multivariate arithmetic Tutte polynomial

DOI10.1090/S0002-9947-2014-06092-3zbMath1300.05133OpenAlexW1977826931MaRDI QIDQ3190809

Luca Moci, Petter Brändén

Publication date: 19 September 2014

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-2014-06092-3

zbMATH Keywords

matroidPotts modelchromatic polynomialTutte polynomialabelian grouparithmetic matroidtoric arrangementquasi-polynomialmultivariate Tutte polynomial

Mathematics Subject Classification ID

Graph polynomials (05C31) Arrangements of points, flats, hyperplanes (aspects of discrete geometry) (52C35) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Combinatorial aspects of matroids and geometric lattices (05B35) Abelian groups (20K99)

Related Items (31)

Universal Tutte characters via combinatorial coalgebras ⋮ Matroids Over a Ring ⋮ Poincaré polynomial of elliptic arrangements is not determined by the Tutte polynomial ⋮ Orientable arithmetic matroids ⋮ The geometry of geometries: matroid theory, old and new ⋮ Group actions on semimatroids ⋮ Combinatorics of certain abelian Lie group arrangements and chromatic quasi-polynomials ⋮ On the cohomology of arrangements of subtori ⋮ Eulerian polynomials for subarrangements of Weyl arrangements ⋮ On the Tutte-Krushkal-Renardy polynomial for cell complexes ⋮ Polyhedra and parameter spaces for matroids over valuation rings ⋮ The monoid of monotone functions on a poset and quasi-arithmetic multiplicities for uniform matroids ⋮ Representations of torsion-free arithmetic matroids ⋮ Face module for realizable Z-matroids ⋮ Topology of arrangements and representation stability. Abstracts from the workshop held January 14--20, 2018 ⋮ The homotopy type of elliptic arrangements ⋮ A convolution formula for Tutte polynomials of arithmetic matroids and other combinatorial structures ⋮ Toric arrangements associated to graphs ⋮ Products of arithmetic matroids and quasipolynomial invariants of CW-complexes ⋮ The integer cohomology algebra of toric arrangements ⋮ Representations of weakly multiplicative arithmetic matroids are unique ⋮ On powers of Plücker coordinates and representability of arithmetic matroids ⋮ Geometric realizations and duality for Dahmen-Micchelli modules and De Concini-Procesi-Vergne modules ⋮ Orlik-Solomon type presentations for the cohomology algebra of toric arrangements ⋮ Cohomology of complements of toric arrangements associated with root systems ⋮ Two examples of toric arrangements ⋮ Combinatorics of toric arrangements ⋮ Stanley-Reisner rings for symmetric simplicial complexes, \(G\)-semimatroids and abelian arrangements ⋮ The Arithmetic Tutte polynomial of two matrices associated to Trees ⋮ An equivalent formulation of chromatic quasi-polynomials ⋮ Splines, lattice points, and arithmetic matroids

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Ehrhart polynomial and arithmetic Tutte polynomial
• Computing the Tutte polynomial of a hyperplane arragement
• Affine and toric hyperplane arrangements
• Graph colorings, flows and arithmetic Tutte polynomial
• Arithmetic matroids, the Tutte polynomial and toric arrangements
• Arrangements, channel assignments, and associated polynomials
• On the Tutte-Krushkal-Renardy polynomial for cell complexes
• The Tutte polynomial
• Characteristic polynomials of subspace arrangements and finite fields
• A Tutte polynomial for toric arrangements
• A Contribution to the Theory of Chromatic Polynomials

This page was built for publication: The multivariate arithmetic Tutte polynomial