The weighted binomial sum $f_m(r)=2^{-r}\sum_{i=0}^r\binom{m}{i}$ arises in coding theory and information theory. We prove that,for $m\not \in\{0,3,6,9,12\}$, the maximum value of $f_m(r)$ with $0\leqslant r\leqslant m$ occurs when $r=\lfloor m/3\rfloor+1$. also show this is asymptotic to $\frac{3}{\sqrt{{\pi}m}}\left(\frac{3}{2}\right)^m$ as $m\to\infty$.

Given a sequence of n real numbers a1, a2, a3, . . . , an, the maximum segment sum problem is that of determining indices i and j (1 ≤ i ≤ j ≤ n) such that the sum s(i, j) = ai + ai+1 + . . . + aj is a maximum. Monotone matrices were shown to be remarkably effective in solving several geometric optimization problems. The surprise is that it can also be applied to the above problem as we show he...

User selection is necessary for multiuser multiple-input multiple-output (MIMO) downlink systems with block diagonalization (BD) due to the limited free spatial transmit dimensions. The pure user selection algorithms can be improved by performing receive antenna selection (RAS) to increase sum rate. In this paper, a joint user and antenna selection algorithm, which performs user selection for s...

A Nordhaus-Gaddum-type result is a (tight) lower or upper bound on the sum or product of a parameter of a graph and its complement. In this paper we study Nordhaus-Gaddum-type results for total domination. We examine the sum and product of γt(G1) and γt(G2) where G1 ⊕G2 = K(s, s), and γt is the total domination number. We show that the maximum value of the sum of the total domination numbers of...

A well-known formula of Tutte and Berge expresses the size of a maximum matching in a graph G in terms of what is usually called the deficiency. A subset X of V (G) for which this deficiency is attained is called a Tutte set of G. While much is known about maximum matchings, less is known about the structure of Tutte sets. We explored the structural aspects of Tutte sets in another paper. Here ...