| Texto completo | |
| Autor(es): |
Fernandes, Cristina G.
[1]
;
de Pina, Jose C.
[1]
;
Alfonsin, Jorge Luis Ramirez
[2]
;
Robins, Sinai
[1]
Número total de Autores: 4
|
| Afiliação do(s) autor(es): | [1] Univ Sao Paulo, Inst Matemat & Estat, BR-05508090 Sao Paulo - Brazil
[2] Univ Montpellier, CNRS, IMAG, Montpellier - France
Número total de Afiliações: 2
|
| Tipo de documento: | Artigo Científico |
| Fonte: | DISCRETE & COMPUTATIONAL GEOMETRY; v. 65, n. 1 APR 2020. |
| Citações Web of Science: | 1 |
| Resumo | |
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 (NNI) move on graphs and a naturally arising piecewise unimodular transformation. We provide a generalization of the context in which the NNI moves appear, to connected graphs with the same degree sequence. We also show that, up to a dilation factor of 4 and an integer translation, all of these Liu-Osserman polytopes are reflexive. (AU) | |
| Processo FAPESP: | 15/10323-7 - Matroides e grafos |
| Beneficiário: | Cristina Gomes Fernandes |
| Modalidade de apoio: | Auxílio à Pesquisa - Pesquisador Visitante - Internacional |
| Processo FAPESP: | 13/03447-6 - Estruturas combinatórias, otimização e algoritmos em Teoria da Computação |
| Beneficiário: | Carlos Eduardo Ferreira |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |