2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/158064Among all states on the algebra of non-commutative polynomials, we characterize the ones that have monic orthogonal polynomials. The characterizations involve recursion relations, Hankel-type determinants, and a representation as a joint distribution of operators on a Fock space.10 pagesCombinatoricsOperator AlgebrasPrimary 05E35; Secondary 46Ntext