منابع مشابه
The Honeycomb Conjecture
This paper gives a proof of the classical honeycomb conjecture: any partition of the plane into regions of equal area has perimeter at least that of the regular hexagonal honeycomb tiling.
متن کاملOn the Application of the Honeycomb Conjecture to the Bee’s Honeycomb∗†
In a recent paper, Aidan Lyon and Mark Colyvan have proposed an explanation of the structure of the bee’s honeycomb based on the mathematical Honeycomb Conjecture. This explanation has instantly become one of the standard examples in the philosophical debate on mathematical explanations of physical phenomena. In this critical note, I argue that the explanation is not scientifically adequate. Th...
متن کاملThe Honeycomb Model of the Berenstein-zelevinsky Polytope I. Klyachko’s Saturation Conjecture
Recently Klyachko [K] has given linear inequalities on triples (λ, μ, ν) of dominant weights of GLn(C) necessary for the the corresponding Littlewood-Richardson coefficient dim(Vλ⊗Vμ⊗Vν) GLn(C) to be positive. We show that these conditions are also sufficient, which was known as the saturation conjecture. In particular this proves Horn’s conjecture from 1962, giving a recursive system of inequa...
متن کاملTHE HONEYCOMB MODEL OF GLn(C) TENSOR PRODUCTS I: PROOF OF THE SATURATION CONJECTURE
Recently Klyachko [Kl] has given linear inequalities on triples (λ, μ, ν) of dominant weights of GLn(C) necessary for the the corresponding Littlewood-Richardson coefficient dim(Vλ⊗Vμ⊗Vν) GLn(C) to be positive. We show that these conditions are also sufficient, which was known as the saturation conjecture. In particular this proves Horn’s conjecture from 1962, giving a recursive system of inequ...
متن کاملThe Auslander-Reiten Conjecture for Group Rings
This paper studies the vanishing of $Ext$ modules over group rings. Let $R$ be a commutative noetherian ring and $ga$ a group. We provide a criterion under which the vanishing of self extensions of a finitely generated $Rga$-module $M$ forces it to be projective. Using this result, it is shown that $Rga$ satisfies the Auslander-Reiten conjecture, whenever $R$ has finite global dimension and $ga...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2001
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s004540010071