Add to ORKGTwo combinatorial statistics, the pyramid weight and the number of exterior pairs, are investigated on the set of Dyck paths. Explicit formulae are given for the generating functions of Dyck paths of prescribed pyramid weight and prescribed number of exterior pairs. The proofs are combinatorial and rely on the method of q-grammars as well as on two new q-analogues of the Catalan numbers derived from statistics on noncrossing partitions. Connections with the combinatorics of Motzkin paths are pointed out
We relate the combinatorics of periodic generalized Dyck and Motzkin paths to the cluster coefficien...
We study various aspects of lattice path combinatorics. A new object, which has Dyck paths as its su...
AbstractA k-generalized Dyck path of length n is a lattice path from (0,0) to (n,0) in the plane int...
AbstractTwo combinatorial statistics, the pyramid weight and the number of exterior pairs, are inves...
The number of down-steps between pairs of up-steps in kt-Dyck paths, a generalization of Dyck paths ...
AMS Subject Classication: 05A15, 05A05 Abstract. In this paper we introduce a new bijection from the...
AMS Subject Classification: 05A15, 05A05 Abstract. In this paper we introduce a new bijection from t...
ABSTRACT: In the present paper we consider the statistic \number of udu's " in Dyck paths....
AbstractThe Catalan numbers occur ubiquitously in combinatorics. R. Stanley’s book Enumerative Combi...
22 pages, 3 figures, 2 tablesWe introduce and study the new combinatorial class of Dyck paths with a...
International audienceWe investigate new equivalence relations on the set $\mathcal{D}_n$ of Dyck pa...
We construct a formal power series on several variables that encodes many statis-tics on non-decreas...
AbstractIn this paper we shall give the generating functions for the enumeration of non-crossing par...
We examine combinatorial parameters of three models of random lattice walks with up and down steps. ...
We relate the combinatorics of periodic generalized Dyck and Motzkin paths to the cluster coefficien...
We study various aspects of lattice path combinatorics. A new object, which has Dyck paths as its su...
AbstractA k-generalized Dyck path of length n is a lattice path from (0,0) to (n,0) in the plane int...
AbstractTwo combinatorial statistics, the pyramid weight and the number of exterior pairs, are inves...
The number of down-steps between pairs of up-steps in kt-Dyck paths, a generalization of Dyck paths ...
AMS Subject Classication: 05A15, 05A05 Abstract. In this paper we introduce a new bijection from the...
AMS Subject Classification: 05A15, 05A05 Abstract. In this paper we introduce a new bijection from t...
ABSTRACT: In the present paper we consider the statistic \number of udu's " in Dyck paths....
AbstractThe Catalan numbers occur ubiquitously in combinatorics. R. Stanley’s book Enumerative Combi...
22 pages, 3 figures, 2 tablesWe introduce and study the new combinatorial class of Dyck paths with a...
International audienceWe investigate new equivalence relations on the set $\mathcal{D}_n$ of Dyck pa...
We construct a formal power series on several variables that encodes many statis-tics on non-decreas...
AbstractIn this paper we shall give the generating functions for the enumeration of non-crossing par...
We examine combinatorial parameters of three models of random lattice walks with up and down steps. ...
We relate the combinatorics of periodic generalized Dyck and Motzkin paths to the cluster coefficien...
We study various aspects of lattice path combinatorics. A new object, which has Dyck paths as its su...
AbstractA k-generalized Dyck path of length n is a lattice path from (0,0) to (n,0) in the plane int...