منابع مشابه
Dense packing on uniform lattices
We study the Hard Core Model on the graphs G obtained from Archimedean tilings i.e. configurations in {0,1} with the nearest neighbor 1’s forbidden. Our particular aim in choosing these graphs is to obtain insight to the geometry of the densest packings in a uniform discrete set-up. We establish density bounds, optimal configurations reaching them in all cases, and introduce a probabilistic cel...
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Let X be a locally finite tree, and let G = Aut(X). Then G is a locally compact group. We show that if X has more than one end, and if G contains a discrete subgroup Γ such that the quotient graph of groups Γ\\X is infinite but has finite covolume, then G contains a non-uniform lattice, that is, a discrete subgroup Λ such that Λ\G is not compact, yet has a finite G-invariant measure. 0. Notatio...
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A lattice L is uniform, if for any congruence Θ of L, any two congruence classes A and B of Θ are of the same size, that is, |A| = |B| holds. A classical result of R. P. Dilworth represents a finite distributive lattice D as the congruence lattice of a finite lattice L. We show that this L can be constructed as a finite uniform lattice.
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A non-uniform bin packing game is an N-person cooperative game, where the set N is defined by k bins of capacities b1, . . . , bk and n items of sizes a1, . . . , an. The objective function v of a coalition is the maximum total value of the items of that coalition which can be packed to the bins of that coalition. We investigate the taxation model of Faigle and Kern (1993) [2] and show that the...
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Let X be a 2-dimensional right-angled hyperbolic building. We characterise the set of covolumes of uniform lattices in Aut(X). We also show that the group Aut(X) admits an infinite ascending tower of uniform lattices.
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ژورنال
عنوان ژورنال: Journal of Statistical Physics
سال: 2007
ISSN: 0022-4715,1572-9613
DOI: 10.1007/s10955-007-9448-0