منابع مشابه
On the Generalized Lower Bound Conjecture for Polytopes and Spheres
In 1971, McMullen and Walkup posed the following conjecture, which is called the generalized lower bound conjecture: If P is a simplicial d-polytope then its h-vector (h0, h1, . . . , hd) satisfies h0 ≤ h1 ≤ · · · ≤ h⌊ d2 ⌋. Moreover, if hr−1 = hr for some r ≤ d2 then P can be triangulated without introducing simplices of dimension ≤ d− r. The first part of the conjecture was solved by Stanley ...
متن کاملThe Lower and Upper Bound Problems for Cubical Polytopes
We construct a family of cubical polytypes which shows that the upper bound on the number of facets of a cubical polytope (given a fixed number of vertices) is higher than previously suspected. We also formulate a lower bound conjecture for cubical polytopes.
متن کاملLower Bound Theorems and a Generalized Lower Bound Conjecture for balanced simplicial complexes
A (d − 1)-dimensional simplicial complex is called balanced if its underlying graph admits a proper d-coloring. We show that many well-known face enumeration results have natural balanced analogs (or at least conjectural analogs). Specifically, we prove the balanced analog of the celebrated Lower Bound Theorem for normal pseudomanifolds and characterize the case of equality; we introduce and ch...
متن کاملAcknowledgments: 5.2 Lower Bound for General Algorithms
Lower and upper bounds are proved for the time complexity of solving two decision problems in a distributed network in the presence of process failures and inexact information about time. It is assumed that the amount of (real) time between two consecutive steps of a nonfaulty process is at least c1 and at most c2; thus, C = c2=c1 is a measure of the timing uncertainty. It is also assumed that ...
متن کاملMcMullen's Conditions and Some Lower Bounds for General Convex Polytopes
Convex polytopes are the d-dimensional analogues of 2-dimensional convex polygones and 3-dimensional convex polyhedra. A polytope is a bounded convex set in R d that is the intersection of a finite number of closed halfspaces. The faces of a polytope are its intersections with supporting hyperplanes. The/-dimensional faces are called the i-faces and f i ( P ) denotes the number of i-faces of a ...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2019
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2018.12.003