منابع مشابه
Indecomposable Polytopes
The space of summands (with respect to vector addition) of a convex polytope in n dimensions is studied. This space is shown to be isomorphic to a convex pointed cone in Euclidean space. The extreme rays of this cone correspond to similarity classes of indecomposable polytopes. The decomposition of a polytope is described and a bound is given for the number of indecomposable summands needed. A ...
متن کاملPermutation polytopes and indecomposable elements in permutation groups
Each group G of n × n permutation matrices has a corresponding permutation polytope, P (G) := conv(G) ⊂ R. We relate the structure of P (G) to the transitivity of G. In particular, we show that if G has t nontrivial orbits, then min{2t, ⌊n/2⌋} is a sharp upper bound on the diameter of the graph of P (G). We also show that P (G) achieves its maximal dimension of (n − 1) precisely when G is 2-tra...
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We prove that for every k > 1, there exist k-fold coverings of the plane (1) with strips, (2) with axis-parallel rectangles, and (3) with homothets of any fixed concave quadrilateral, that cannot be decomposed into two coverings. We also construct, for every k > 1, a set of points P and a family of disks D in the plane, each containing at least k elements of P , such that no matter how we color...
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We study some relations between a reproducing cone K in a linear space V over a fully ordered field F and the cone I(K) in Hom( V, V) consisting of all operators A such that AK G K. In particular, indecomposable cones are considered.
متن کاملDIRECTLY INDECOMPOSABLE RESIDUATED LATTICES
The aim of this paper is to extend results established by H. Onoand T. Kowalski regarding directly indecomposable commutative residuatedlattices to the non-commutative case. The main theorem states that a residuatedlattice A is directly indecomposable if and only if its Boolean center B(A)is {0, 1}. We also prove that any linearly ordered residuated lattice and anylocal residuated lattice are d...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1974
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1974-0338929-4