In this paper we provide two axiomatizations of the class of idempotent discrete uninorms as conservative binary operations, where an operation is conservative if it always outputs one of its input values. More precisely we first show that the idempotent discrete uninorms are exactly those operations that are conservative, symmetric, and nondecreasing in each variable. Then we show that, in thi...

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 ...