In this article we show how to compute the chromatic quasisymmetric function of indifference graphs from modular law introduced in [19]. We provide an algorithm which works for any that satisfies law, such as unicellular LLT polynomials. When graph has bipartite complement it reduces a planar network, case, prove coefficients elementary basis are positive unimodal polynomials and characterize t...

A gain graph is a graph whose edges are labelled invertibly by gains from a group. Switching is a transformation of gain graphs that generalizes conjugation in a group. A weak chromatic function of gain graphs with gains in a fixed group satisfies three laws: deletion-contraction for links with neutral gain, invariance under switching, and nullity on graphs with a neutral loop. The laws are ana...

A gain graph is a graph whose edges are labelled invertibly by gains from a group. Switching is a transformation of gain graphs that generalizes conjugation in a group. A weak chromatic function of gain graphs with gains in a fixed group satisfies three laws: deletion-contraction for links with neutral gain, invariance under switching, and nullity on graphs with a neutral loop. The laws are ana...

Given an oriented graph G, the modular flow polynomial φG(k) counts the number of nowhere-zero Zk-flows of G. We give a description of the modular flow polynomial in terms of (open) Ehrhart polynomials of lattice polytopes. Using Ehrhart–Macdonald reciprocity we give a combinatorial interpretation for the values of φG at negative arguments which answers a question of Beck and Zaslavsky (Adv Mat...