arXiv subjects

Mike Develin

Publications and source records attributed to Mike Develin.

21 records · Page 2Linked to original sources

arXiv2002

Avoidable sets in groups

In a set equipped with a binary operation, (S,*), a subset U is defined to be avoidable if there exists a partition {A,B} of S such that no element of U is the product of two distinct elements of A or of two distinct elements of B. For more than two decades, avoidable sets in the natural numbers (under addition) have been studied by renowned mathematicians such as Erdos, and a few families of sets have been shown to be avoidable in that setting. In this paper we investigate the generalized notion of an avoidable set and determine the avoidable sets in several families of groups; previous work in this field considered only the case (S, *) = (N, +).

math.CO↗

arXiv2002

Cayley compactifications of abelian groups

Following work of Rieffel, we define the Cayley compactification of an abelian group with specified generating set. We investigate its structure using methods from discrete geometry and commutative algebra.

math.CO↗

arXiv2002

On LP-orientations of cubes and crosspolytopes

We show that the Holt-Klee conditions are very insufficient for an orientation of the graph of a polytope to be an LP-orientation in the case of the n-cube. We also give a strengthening of the Holt-Klee conditions which is both necessary and sufficient in the case of the crosspolytope.

math.CO↗