We show that for certain discrete p-perfect groups G, in particular for all pperfect groups of finite cohomological dimension, the loop space on the p-completed classifying space ΩBGp is a retract of the loop spaces on a certain finite complex. For finite vcd groups we provide a bound on the the dimension of such a complex.

We present a simple primal-dual algorithm for computing approximate Nash equilibria in two-person zero-sum sequential games with incomplete information and perfect recall (like Texas Hold’em poker). Our algorithm only performs basic iterations (i.e matvec multiplications, clipping, etc., and no calls to external first-order oracles, no matrix inversions, etc.) and is applicable to a broad class...

The concept of perfection of a polytope was introduced by S. A. Robertson. Intuitively speaking, a polytope P is perfect if and only if it cannot be deformed to a polytope of different shape without changing the action of its symmetry group G(P ) on its face-lattice F (P ). By Rostami’s conjecture, the perfect 4-polytopes form a particular set of Wythoffian polytopes. In the present paper first...

The maximal index of a Euclidean lattice L of dimension n is the maximal index of the sublattices of L spanned by n independent minimal vectors of L. In this paper, we prove that a perfect lattice of maximal index two which is not provided by a cross-section has dimension at most 5.

Abstmct We reveal an equivalence relation between the construction of a new class of low density MDS array codes, that we call B-Code, and a combinatorial problem known as perfect one-factorization of complete graphs. We use known perfect one-factors of complete graphs to create constructions and decoding algorithms for both B-Code and its dual code. B-Code and its dual are optimal in the sense...