Assume that $(N,L)$, is a pair of finite dimensional nilpotent Lie algebras, in which $L$ is non-abelian and $N$ is an ideal in $L$ and also $mathcal{M}(N,L)$ is the Schur multiplier of the pair $(N,L)$. Motivated by characterization of the pairs $(N,L)$ of finite dimensional nilpotent Lie algebras by their Schur multipliers (Arabyani, et al. 2014) we prove some properties of a pair of nilpoten...

Motivated by a conjecture of Liang [Y.-C. Liang. Anti-magic labeling of graphs. PhD thesis, National Sun Yat-sen University, 2013.], we introduce a restricted path packing problem in bipartite graphs that we call a V-free 2-matching. We verify the conjecture through a weakening of the hypergraph matching problem. We close the paper by showing that it is NP-complete to decide whether one of the ...

We investigate the representation of a symmetric group Sn on the homology of its Quillen complex at a prime p. For homology groups in small codimension, we derive an explicit formula for this representation in terms of the representations of symmetric groups on homology groups of p-uniform hypergraph matching complexes. We conjecture an explicit formula for the representation of Sn on the top h...

‎The textit{metric dimension} of a connected graph $G$ is the minimum number of vertices in a subset $B$ of $G$ such that all other vertices are uniquely determined by their distances to the vertices in $B$‎. ‎In this case‎, ‎$B$ is called a textit{metric basis} for $G$‎. ‎The textit{basic distance} of a metric two dimensional graph $G$ is the distance between the elements of $B$‎. ‎Givi...

This is a summary on verbal subgroups in the groups T(∞, K) and UT(∞, K) of infinite dimensional triangular and unitriangular matrices over a field K, |K| > 2. The characterization of the lattices of verbal subgroups in these groups is presented, and the width of verbal subgroups generated by non-commutators, powers and (generalized) Engel words is given [2, 3, 4]. The groups T(∞, K) and UT(∞, ...

DIXtrac is a program that automatically characterizes the performance of modern disk drives. This report describes and validates DIXtrac's algorithms, which extract accurate values for over 100 performance-critical parameters in 2 { 6 minutes without human intervention or special hardware support. The extracted data include detailed layout and geometry information, mechanical timings, cache man...

A combinatorial characterization of a non–singular Hermitian variety of the finite 3-dimensional projective space via its intersection numbers with respect to lines and planes is given.