A two-family extremal problem in hamming space

A two-family extremal problem in hamming space

(1) Let S~ denote the set of those systems. We consider the function M(m, 8)a-max{iA[ [BI: (A, B)e S'~} (2) and prove the following Theorem: For m = 1, 2 ..... maxo.~s.~ m M(m, 8) = 22n, if m = 2n or m = 2n + 1. The maximum is assumed for 8 = n.

A nonlinear extremal problem on the Hardy space

and the compression of Toeplitz operators to the model spaces H ΘH. In the above, D denotes the open unit disk, ∂D denotes the unit circle, ψ is a rational function whose poles do not lie on ∂D, H is the classical Hardy space [11, 19, 24], and Θ is a finite Blaschke product. We refer to ψ as the kernel of the extremal problems (1) and (2). Since the focus of this paper is primarily on H, we let...

Extremal Sets Minimizing Dimension-normalized Boundary in Hamming Graphs∗

We prove that the set of first k vertices of a Hamming graph in reverse-lexicographic order constitutes an extremal set minimizing the dimension-normalized edge-boundary over all kvertex subsets of the graph. This generalizes a result of Lindsey and can be used to prove a tight lower bound for the isoperimetric number and the bisection width of arrays.

Extremal Sets Minimizing Dimension-Normalized Boundary in Hamming Graphs

On the Construction of Solutions of a Discrete Isoperimetric Problem in Hamming Space

This article is a study of the solution set of a discrete isoperimetric problem.