Skip to Main content Skip to Navigation
Conference papers

Structure of spaces of rhombus tilings in the lexicograhic case

Abstract : 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.
Complete list of metadata

Cited literature [9 references]  Display  Hide  Download
Contributor : Coordination Episciences Iam Connect in order to contact the contributor
Submitted on : Friday, August 14, 2015 - 11:37:09 AM
Last modification on : Saturday, September 11, 2021 - 3:18:22 AM
Long-term archiving on: : Sunday, November 15, 2015 - 10:59:06 AM


Publisher files allowed on an open archive



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⟩



Record views


Files downloads