Very recently, we proposed the row-monomial distributed orthogonal space-time block codes (DOSTBCs) and showed that the row-monomial DOSTBCs achieved approximately twice higher bandwidth efficiency than the repetitionbased cooperative strategy [1]. However, we imposed two limitations on the row-monomial DOSTBCs. The first one was that the associated matrices of the codes must be row-monomial. T...

For a finitely generated group G, we construct representation of G explicitly. Along the way, describe structure 2-cocycles G. We also prove characterization monomial projective representations nilpotent groups and polycyclic whose are finite dimensional.

Convex hulls of monomials have been widely studied in the literature, and monomial convexifications are implemented in global optimization software for relaxing polynomials. However, there has been no study of the error in the global optimum from such approaches. We give bounds on the worst-case error for convexifying a monomial over subsets of [0, 1]. This implies additive error bounds for rel...

Using the Beilinson-Lusztig-MacPherson construction of the quantized enveloping algebra of gln and its associated monomial basis, we investigate q-Schur algebras Sq(n, r) as “little quantum groups”. We give a presentation for Sq(n, r) and obtain a new basis for the integral q-Schur algebra Sq(n, r), which consists of certain monomials in the original generators. Finally, when n > r, we interpre...

We provide a new combinatorial approach to study the minimal free resolutions of edge ideals, that is, quadratic square-free monomial ideals. With this method we can recover most of the known results on resolutions of edge ideals with fuller generality, and at the same time, obtain new results. Past investigations on the resolutions of edge ideals usually reduced the problem to computing the di...

Alexander duality has, in the past, made its way into commutative algebra through Stanley-Reisner rings of simplicial complexes. This has the disadvantage that one is limited to squarefree monomial ideals. The notion of Alexander duality is generalized here to arbitrary monomial ideals. It is shown how this duality is naturally expressed by Bass numbers, in their relations to the Betti numbers ...

All known direct constructions of designs over finite fields arise by subgroups of the normalizer of a Singer cycle, by lifted special linear groups, or lifted general linear groups. Other types of non-trivial automorphism groups for which designs over finite fields do exist have not been mentioned so far. In this paper we construct the first non-trivial designs over finite fields admitting the...