For a self-small abelian group A of torsion-free rank 1, we characterize A-reflexive abelian groups which are induced by the contravariant functor Hom(−, A) in two cases: the range of Hom(−, A) is the category of all abelian groups, respectively the range of Hom(−, A) is the category of all left E-modules, where E is the endomorphism ring of A.

In this paper, we mainly investigate a revised induction funtor to study Hom-Doi-Hopf modules and the coinvariant for Hom-Hopf comodule algebras.

The Hom complex of homomorphisms between two graphs was originally introduced to provide topological lower bounds on the chromatic number of graphs. In this paper we introduce new methods for understanding the topology of Hom complexes, mostly in the context of Γ-actions on graphs and posets (for some group Γ). We view the Hom(T, •) and Hom(•, G) as functors from graphs to posets, and introduce...

by John Alan Engbers For graphs G and H, an H-coloring of G, or homomorphism from G to H, is an edge-preserving map from the vertices of G to the vertices of H. H-colorings generalize such graph theory notions as proper colorings and independent sets. In this dissertation, we consider four questions involving H-colorings of graphs. Recently, Galvin [27] showed that the maximum number of indepen...

Using autologous serum for the serological analysis of recombinantly expressed clones (SEREX) from a cDNA derived from a human mela noma, several new melanoma antigens were identified that are immuno genic in the autologous host. Sequence analysis revealed that one of these antigens, HOM-MEL-40, was coded for by the SSX2 gene, which has recently been described to be involved in the t(X;18) tran...