scholarly journals The complex of maximal lattice free simplices

1994 ◽  
Vol 66 (1-3) ◽  
pp. 273-281 ◽  
Author(s):  
Imre Bárány ◽  
Roger Howe ◽  
Herbert E. Scarf
Keyword(s):  
Maximal Lattice

scholarly journals Dual skew Heyting almost distributive lattices

2019 ◽  
Vol 4 (1) ◽  
pp. 151-162 ◽  
Author(s):  
Berhanu Assaye ◽  
Mihret Alamneh ◽  
Lakshmi Narayan Mishra ◽  
Yeshiwas Mebrat
Keyword(s):  
Equivalence Class ◽  
Equivalence Relation ◽  
Congruence Relation ◽  
Heyting Algebra ◽  
Congruence Class ◽  
Distributive Lattices ◽  
Lattice Image ◽  
Principal Ideals ◽  
Maximal Lattice

AbstractIn this paper, we introduce the concept of dual skew Heyting almost distributive lattices (dual skew HADLs) and characterise it in terms of dual HADL. We define an equivalence relation θ on a dual skew HADL L and prove that θ is a congruence relation on the equivalence class [x]θ so that each congruence class is a maximal rectangular subalgebra and the quotient [y]θ/θ is a maximal lattice image of [x]θ for any y ∈ [x]θ. Moreover, we show that if the set PI (L) of all the principal ideals of an ADL L with 0 is a dual skew Heyting algebra then L becomes a dual skew HADL. Further we present different conditions on which an ADL with 0 becomes a dual skew HADL.

scholarly journals Maximal Lattice-Free Convex Sets in Linear Subspaces

2010 ◽  
Vol 35 (3) ◽  
pp. 704-720 ◽  
Author(s):  
Amitabh Basu ◽  
Michele Conforti ◽  
Gérard Cornuéjols ◽  
Giacomo Zambelli
Keyword(s):  
Convex Sets ◽  
Linear Subspaces ◽  
Maximal Lattice

scholarly journals Maximal Lattice-Free Polyhedra: Finiteness and an Explicit Description in Dimension Three

2011 ◽  
Vol 36 (4) ◽  
pp. 721-742 ◽  
Author(s):  
Gennadiy Averkov ◽  
Christian Wagner ◽  
Robert Weismantel
Keyword(s):  
Explicit Description ◽  
Maximal Lattice

scholarly journals A Note on Maximal Lattice Growth in SO(1,n)

2012 ◽  
Vol 2013 (16) ◽  
pp. 3722-3731 ◽  
Author(s):  
Jean Raimbault
Keyword(s):  
Maximal Lattice

scholarly journals The Sorting Order on a Coxeter Group

2008 ◽  
Vol DMTCS Proceedings vol. AJ,... (Proceedings) ◽  
Author(s):  
Drew Armstrong
Keyword(s):  
Distributive Lattice ◽  
Partial Order ◽  
Coxeter Group ◽  
Bruhat Order ◽  
Distributive Lattices ◽  
Coxeter System ◽  
Maximal Lattice ◽  
International Audience ◽  
The Way

International audience Let $(W,S)$ be an arbitrary Coxeter system. For each sequence $\omega =(\omega_1,\omega_2,\ldots) \in S^{\ast}$ in the generators we define a partial order― called the $\omega \mathsf{-sorting order}$ ―on the set of group elements $W_{\omega} \subseteq W$ that occur as finite subwords of $\omega$ . We show that the $\omega$-sorting order is a supersolvable join-distributive lattice and that it is strictly between the weak and strong Bruhat orders on the group. Moreover, the $\omega$-sorting order is a "maximal lattice'' in the sense that the addition of any collection of edges from the Bruhat order results in a nonlattice. Along the way we define a class of structures called $\mathsf{supersolvable}$ $\mathsf{antimatroids}$ and we show that these are equivalent to the class of supersolvable join-distributive lattices.

scholarly journals The topological structure of maximal lattice free convex bodies: The general case

1998 ◽  
Vol 80 (1) ◽  
pp. 1-15 ◽  
Author(s):  
I. Bárány ◽  
H. E. Scarf ◽  
D. Shallcross
Keyword(s):  
Topological Structure ◽  
Convex Bodies ◽  
Maximal Lattice
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