A graph G is said to be hom-idempotent if there is a homomorphism from G2 to G, and weakly hom-idempotent if for some n ≥ 1 there is a homomorphism from Gn+1 to Gn. Larose et al. (1998) proved that Kneser graphs KG(n, k) are not weakly hom-idempotent for n ≥ 2k + 1, k ≥ 2. For s ≥ 2, we characterize all the shifts (i.e., automorphisms of the graph that map every vertex to one of its neighbors) ...

Valuation based systems verifying an idem­ potent property are studied. A partial or­ der is defined between the valuations giving them a lattice structure. Then, two different strategies are introduced to represent valu­ ations: as infimum of the most informative valuations or as supremum of the least in­ formative ones. It is studied how to carry out computations with both representations in ...

Using the characterization of the idempotents of a narrow-sense primitive binary BCH code, we are able to give classes of such codes whose minimum distance reaches the BCH bound. Let be a primitive element of GF(2 m). We denote R n = GF(2))x]=(x n ? 1), n = 2 m ? 1. 1 Binary BCH codes and locator polynomials 1.1 Primitive binary BCH codes For our purpose we only need to deene a particular class...

For a l m o s t as l o n g as a t t e m p t s a t p r o v i n g theorems by mach ines have been made, a c r i t i c a l p r o b l e m has been w e l l known: E q u a t i o n a l a x i o m s , i f l e f t w i t h o u t p r e c a u t i o n s i n t he d a t a base o f a n a u t o m a t i c t heo rem p r o v e r (ATP) , w i l l f o r c e the ATP t o g o a s t r a y . Four approaches t o cope w i t ...

A short proof of the characterization of idempotent subreducts of semimodules over commutative semirings is presented. It says that an idempotent algebra embeds into a semimodule over a commutative semiring, if and only if it belongs to the variety of Szendrei modes.