Direct limits of cyclically ordered groups

Generalized Covering Groups and Direct Limits

generalized covering groups and direct limits

Direct Products of Ordered Abelian Groups

In this paper we study some theories of direct products of ordered abelian

Pattern avoidance in cyclically ordered structures

We generalize the notion of pattern avoidance to arbitrary functions on ordered sets, and consider specifically three scenarios for permutations: linear, cyclic and hybrid, the first one corresponding to classical permutation avoidance. The cyclic modification allows for circular shifts in the entries. Using two bijections, both ascribable to both Deutsch and Krattenthaler independently, we sin...

Minmax relations for cyclically ordered digraphs

We prove a range of minmax theorems about cycle packing and covering in digraphs whose vertices are cyclically ordered, a notion promoted by Bessy and Thomassé in their beautiful proof of the following conjecture of Gallai: the vertices of a strongly connected digraph can be covered by at most as many cycles as the stability number. The results presented here provide relations between cycle pac...