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 ...

An idempotent operator E in a Hilbert space H(E2= 1) is written as a 2 × 2 matrix in terms of the orthogonal decomposition H=R(E)⊕R(E)⊥(R(E) is the range of E) as (Formula Presented). We study the sets of idempotents that ...

For a fixed n > 2, we study the set of generalized idempotents, which are operators satisfying Tn+1 = T. Also the subsets † , of operators such that Tn−1 is the Moore–Penrose pseudo-inverse of T, and , of operators such ...

The existence of idempotent elements in plenary train algebras of rank greater than 3, is an open problem to be solved. J. Carlos Gutierrez's results on plenary train algebras in Gutierrez (2000) are based on the underlying ...

In this paper we study plenary train algebras of arbitrary rank. We show that for most parameter choices of the train identity, the additional identity (x2 − ω(x)x)2 = 0 is satisfied. We also find sufficient conditions ...

We consider an evolution algebra which corresponds to a bisexual population with a set of females partitioned into finitely many different types and the males having only one type. We study basic properties of the algebra. ...