New Bounds for Hypercube Slicing Numbers
نویسندگان
چکیده
What is the maximum number of edges of the d-dimensional hypercube, denoted by S d k , that can be sliced by k hyperplanes? This question on combinatorial properties of Euclidean geometry arising from linear separability considerations in the theory of Perceptrons has become an issue on its own. We use computational and combinatorial methods to obtain new bounds for S d k , d 8. These strengthen earlier results on hypercube cut numbers.
منابع مشابه
Coefficient Bounds for Analytic bi-Bazileviv{c} Functions Related to Shell-like Curves Connected with Fibonacci Numbers
In this paper, we define and investigate a new class of bi-Bazilevic functions related to shell-like curves connected with Fibonacci numbers. Furthermore, we find estimates of first two coefficients of functions belonging to this class. Also, we give the Fekete-Szegoinequality for this function class.
متن کاملA New Parallel Matrix Multiplication Method Adapted on Fibonacci Hypercube Structure
The objective of this study was to develop a new optimal parallel algorithm for matrix multiplication which could run on a Fibonacci Hypercube structure. Most of the popular algorithms for parallel matrix multiplication can not run on Fibonacci Hypercube structure, therefore giving a method that can be run on all structures especially Fibonacci Hypercube structure is necessary for parallel matr...
متن کاملPolychromatic Colorings on the Hypercube
Given a subgraph G of the hypercube Qn, a coloring of the edges of Qn such that every embedding of G contains an edge of every color is called a G-polychromatic coloring. The maximum number of colors with which it is possible to G-polychromatically color the edges of any hypercube is called the polychromatic number of G. To determine polychromatic numbers, it is only necessary to consider a str...
متن کاملAverage Sensitivity and Noise Sensitivity of Polynomial Threshold Functions
We give the first non-trivial upper bounds on the average sensitivity and noise sensitivity of degree-d polynomial threshold functions (PTFs). These bounds hold both for PTFs over the Boolean hypercube {−1, 1}n and for multilinear PTFs over R n under the standard n-dimensional Gaussian distribution N (0, In). Our bound on the Boolean average sensitivity of PTFs represents progress towards the r...
متن کاملError Bounds for Some Semidefinite Programming Approaches to Polynomial Minimization on the Hypercube
We consider the problem of minimizing a polynomial on the hypercube [0, 1] and derive new error bounds for the hierarchy of semidefinite programming approximations to this problem corresponding to the Positivstellensatz of Schmüdgen [26]. The main tool we employ is Bernstein approximations of polynomials, which also gives constructive proofs and degree bounds for positivity certificates on the ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2001