Structure of spaces of rhombus tilings in the lexicograhic case - Archive ouverte HAL Accéder directement au contenu
Communication Dans Un Congrès Discrete Mathematics and Theoretical Computer Science Année : 2005

Structure of spaces of rhombus tilings in the lexicograhic case

Résumé

Rhombus tilings are tilings of zonotopes with rhombohedra. We study a class of \emphlexicographic rhombus tilings of zonotopes, which are deduced from higher Bruhat orders relaxing the unitarity condition. Precisely, we fix a sequence $(v_1, v_2,\dots, v_D)$ of vectors of $ℝ^d$ and a sequence $(m_1, m_2,\dots, m_D)$ of positive integers. We assume (lexicographic hypothesis) that for each subsequence $(v_{i1}, v_{i2},\dots, v_{id})$ of length $d$, we have $det(v_{i1}, v_{i2},\dots, v_{id}) > 0$. The zonotope $Z$ is the set $\{ Σα _iv_i 0 ≤α _i ≤m_i \}$. Each prototile used in a tiling of $Z$ is a rhombohedron constructed from a subsequence of d vectors. We prove that the space of tilings of $Z$ is a graded poset, with minimal and maximal element.
Fichier principal
Vignette du fichier
dmAE0129.pdf (229.63 Ko) Télécharger le fichier
Origine Fichiers éditeurs autorisés sur une archive ouverte
Loading...

Dates et versions

hal-01184356 , version 1 (14-08-2015)

Identifiants

Citer

Éric Rémila. Structure of spaces of rhombus tilings in the lexicograhic case. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. pp.145-150, ⟨10.46298/dmtcs.3400⟩. ⟨hal-01184356⟩
103 Consultations
646 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More