We study the problem of finding zero-sum blocks in bounded-sum sequences, which was introduced by Caro, Hansberg, and Montejano. Caro et al. determine minimum $\{-1,1\}$-sequence length for when there exist $k$ consecutive terms that sum to zero. corresponding sequence set $\{-1,1\}$ is replaced $\{-r,s\}$ arbitrary positive integers $r$ $s.$ This confirms a conjecture theirs. also construct $\...

Let Fq be the finite field of q elements. Let H ⊆ Fq be a multiplicative subgroup. For a positive integer k and element b ∈ Fq, we give a sharp estimate for the number of k-element subsets of H which sum to b.

Between 1952 and 1954 Amitsur and Kurosh initiated the general theory of radicals in various contexts. In the case of all groups some interesting results concerning radicals were obtained by Kurosh, Shchukin, Ryabukhin, Gardner and others. In this paper we are going to examine radical theory in the class of all finite groups. This strong restriction gives chance to obtain stronger results, then...

In this paper, we obtain an explicit formula for the number of zero-sum k-element subsets in any finite abelian group.

in this paper, we show that every element of a discrete module is a sum of two units if and only if its endomorphism ring has no factor ring isomorphic to $z_{2}$. we also characterize unit sum number equal to two for the endomorphism ring of quasi-discrete modules with finite exchange property.

We solve the following problem: Can an undirected weighted graph G be partitioned into two non-empty induced subgraphs satisfying minimum constraints for the sum of edge weights at vertices of each subgraph? We show that this is possible for all constraints a(x), b(x) satisfying dG(x) ≥ a(x) + b(x) + 2WG(x), for every vertex x, where dG(x),WG(x) are, respectively, the sum and maximum of inciden...

Cooperative transmission schemes are used in wireless networks to improve the spectral efficiency. In a multi-cell environment, other cell interference (OCI) degrades the performance of wireless systems. In this paper, we study the performance of downlink sum rate for cell-edge users in a multi-cell environment under base station cooperation. The base-stations coordinate their transmission to t...

We introduce joins of signed graphs and explore the chromatic number all-positive all-negative joins. prove an analogue to theorem that join two equals sum their numbers. Given graphs, is usually less than numbers, by amount depends on new concept deficiency a signed-graph coloration.