Cubic graphs, their Ehrhart quasi-polynomials, and a scissors congruence phenomenon

Autor:	Fernandes, Cristina G., de Pina, José C., Alfonsín, Jorge Luis Ramírez, Robins, Sinai
Rok vydání:	2018
Předmět:	Mathematics - Combinatorics Computer Science - Discrete Mathematics
Druh dokumentu:	Working Paper
Popis:	The scissors congruence conjecture for the unimodular group is an analogue of Hilbert's third problem, for the equidecomposability of polytopes. Liu and Osserman studied the Ehrhart quasi-polynomials of polytopes naturally associated to graphs whose vertices have degree one or three. In this paper, we prove the scissors congruence conjecture, posed by Haase and McAllister, for this class of polytopes. The key ingredient in the proofs is the nearest neighbor interchange on graphs and a naturally arising piecewise unimodular transformation. Comment: 17 pages, with 10 figures, and a table
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1802.07164 Zobrazit plný text záznamu View this record from Arxiv