Let G be the right-angled Artin group associated to the flag complex Σ and let π : G → Z be its canonical height function. We investigate the presentation theory of the groups Γn = π(nZ) and construct an algorithm that, given n and Σ, outputs a presentation of optimal deficiency on a minimal generating set, provided Σ is triangle-free; the deficiency tends to infinity as n → ∞ if and only if th...

nowadays, many antibiotics are being used to control infectious diseases. inappropriate use of antibiotics leads to emergence of resistant bacteria and problems such as a prolonged course of treatment. medicinal plants and their derivatives, as a good source of treatment, are effective against drug resistance. in this study we have evaluated the antimicrobial activity of herbal essential oils o...

We describe a minimal unstable module presentation over the Steenrod algebra for the odd-primary cohomology of infinitedimensional complex projective space and apply it to obtain a minimal algebra presentation for the cohomology of the classifying space of the infinite unitary group. We also show that there is a unique Steenrod module structure on any unstable cyclic module that has dimension o...

The direct product of a free group and a polycyclic group is known to be coherent. This paper shows that every finitely generated subsemigroup of the direct product of a virtually free group and an abelian group admits a finite Malcev presentation. (A Malcev presentation is a presentation of a special type for a semigroup that embeds into a group. A group is virtually free if it contains a free...

We describe various classes of infinitely presented groups that are condensation points in the space of marked groups. A well-known class of such groups consists of finitely generated groups admitting an infinite minimal presentation. We introduce here a larger class of condensation groups, called infinitely independently presentable groups, and establish criteria which allow one to infer that ...

A minimal triangulation of a graph is a chordal graph obtained from adding an inclusion-minimal set of edges to the graph. For permutation graphs, i.e., graphs that are both comparability and cocomparability graphs, it is known that minimal triangulations are interval graphs. We (negatively) answer the question whether every interval graph is a minimal triangulation of a permutation graph. We g...

By Shapley’s (1964) theorem, a matrix game has a saddle point whenever each of its 2 × 2 subgames have one. In other words, all minimal saddle point free (SP-free) matrices are of size 2 × 2. We strengthen this result and show that all locally minimal SP-free matrices are of size 2× 2. In other words, if A is a SP-free matrix in which a saddle point appears after deleting an arbitrary row or co...

The corner polyhedron is described by minimal valid inequalities from maximal lattice-free convex sets. For the Relaxed Corner Polyhedron (RCP) with two free integer variables and any number of non-negative continuous variables, it is known that such facet defining inequalities arise from maximal lattice-free splits, triangles and quadrilaterals. We improve on the tightest known upper bound for...