Generate and manipulate toric quivers, their flow polytopes and associated combinatorial structures.
This code was written to reproduce and augment results in [1], [2], and [3].
Originally written in python, a newer version is written in Macaulay2 to facilitate interfacing wtih other M2 packages such as Graphs, Polyhedra, and NormalToricVarieties.
There is 1 main file at the moment: ThinSincereQuivers.m2 contains routines for generating families of toric quivers, for manipulating the graph and weight structures associated to a given quiver, and for generating and analyzing the combinatorial objects associated to a given quiver.
The main routines in this file are listed in the file m2_version/list_of_fuctions(for a more detailed explanation, see the documentation pages generated by ThinSincereQuivers.m2).
[1] Klaus Altmann, Benjamin Nill, Sabine Schwentner, and Izolda Wiercinska, Flow polytopes and the graph of reflexive polytopes, Discrete Mathematics. 309.16(2009), pp 4992-4999. sciencedirect.com/sceince/article/pii/S0012365X09001162
[2] Lutz Hille, Quivers, cones and polytopes, Linear algebra and its appications, 365:215-237(2003) [3] M'aty'as Domokos and D'aniel Jo'o, On the equations and classification of toric quiver varietites, Proceedings of the Royal Society of Edinburgh, Section A: Mathematics, 146(2):265-295(2016)