We study the moments of orthogonal polynomial sequences (OPS) arising from tridiagonal matrices. We obtain combinatorial information about the sequence of moments of some OPS in terms of Motzkin and Dyck paths, and also in terms of the binomial transform. We then introduce an equivalence relation on the set of Dyck paths and some operations on them. We determine a formula for the cardinality of those equivalence classes, and use this information to obtain a combinatorial formula for the number of Dyck and Motzkin paths of a fixed length
ABSTRACT: In the present paper we consider the statistic \number of udu's " in Dyck paths....
The number of down-steps between pairs of up-steps in $k_t$-Dyck paths, a generalization of Dyck pat...
AbstractThe purpose of this paper is to study the combinatorial and enumerative properties of a new ...
We consider the Motzkin paths which are simple combinatorial objects appearing in many contexts. The...
29 pages, no figures.-- MSC1991 code: Primary 42C05.MR#: MR1789676 (2001m:42047)We present character...
Abstract: Consider lattice paths in the plane allowing the steps (1,1), (1,-1), and (w,0), for some ...
AbstractUsing combinatorial methods, we obtain the explicit polynomials for all elements in an arbit...
Abstract We define a bijection between permutations and valued Dyck paths, namely, Dyck paths whos...
AbstractIn this paper we study the number of humps (peaks) in Dyck, Motzkin and Schröder paths. Rece...
AbstractIn this paper Motzkin numbersMn(which are related to Catalan numbers) are studied. The (know...
We study a family of polynomials in two variables, identifying them as the moments of a two-paramete...
AbstractKasraoui, Stanton and Zeng, and Kim, Stanton and Zeng introduced certain q-analogues of Lagu...
We investigate the sequence $(P_{n}(z))_{n=0}^{\infty}$ of random polynomials generated by the three...
We define sequences MTn and CTn of polynomials associated with Motzkin and Catalan paths, respective...
AbstractWe study the class C of (generalized) orthogonal polynomial sequences {Pn(x)}n=0∞ satisfying...
ABSTRACT: In the present paper we consider the statistic \number of udu's " in Dyck paths....
The number of down-steps between pairs of up-steps in $k_t$-Dyck paths, a generalization of Dyck pat...
AbstractThe purpose of this paper is to study the combinatorial and enumerative properties of a new ...
We consider the Motzkin paths which are simple combinatorial objects appearing in many contexts. The...
29 pages, no figures.-- MSC1991 code: Primary 42C05.MR#: MR1789676 (2001m:42047)We present character...
Abstract: Consider lattice paths in the plane allowing the steps (1,1), (1,-1), and (w,0), for some ...
AbstractUsing combinatorial methods, we obtain the explicit polynomials for all elements in an arbit...
Abstract We define a bijection between permutations and valued Dyck paths, namely, Dyck paths whos...
AbstractIn this paper we study the number of humps (peaks) in Dyck, Motzkin and Schröder paths. Rece...
AbstractIn this paper Motzkin numbersMn(which are related to Catalan numbers) are studied. The (know...
We study a family of polynomials in two variables, identifying them as the moments of a two-paramete...
AbstractKasraoui, Stanton and Zeng, and Kim, Stanton and Zeng introduced certain q-analogues of Lagu...
We investigate the sequence $(P_{n}(z))_{n=0}^{\infty}$ of random polynomials generated by the three...
We define sequences MTn and CTn of polynomials associated with Motzkin and Catalan paths, respective...
AbstractWe study the class C of (generalized) orthogonal polynomial sequences {Pn(x)}n=0∞ satisfying...
ABSTRACT: In the present paper we consider the statistic \number of udu's " in Dyck paths....
The number of down-steps between pairs of up-steps in $k_t$-Dyck paths, a generalization of Dyck pat...
AbstractThe purpose of this paper is to study the combinatorial and enumerative properties of a new ...