منابع مشابه
Dyck path statistics
A wide range of articles dealing with the occurrence of strings in Dyck paths appear frequently in the literature [2], [3], [5], [6], [7] and [11]. A Dyck path of semilength n is a lattice path of N2 running from (0, 0) to (2n, 0), whose allowed steps are the up diagonal step (1, 1) and the down diagonal step (1,−1). These steps are called rise and fall respectively. It is clear that each Dyck ...
متن کاملEnumeration of saturated chains in Dyck lattices
We determine a general formula to compute the number of saturated chains in Dyck lattices, and we apply it to find the number of saturated chains of length 2 and 3. We also compute what we call the Hasse index (of order 2 and 3) of Dyck lattices, which is the ratio between the total number of saturated chains (of length 2 and 3) and the cardinality of the underlying poset.
متن کاملDyck path triangulations and extendability
We introduce the Dyck path triangulation of the cartesian product of two simplices ∆n−1×∆n−1. The maximal simplices of this triangulation are given by Dyck paths, and its construction naturally generalizes to produce triangulations of ∆rn−1 × ∆n−1 using rational Dyck paths. Our study of the Dyck path triangulation is motivated by extendability problems of partial triangulations of products of t...
متن کاملGeneral Results on the Enumeration of Strings in Dyck Paths
Let τ be a fixed lattice path (called in this context string) on the integer plane, consisting of two kinds of steps. The Dyck path statistic “number of occurrences of τ” has been studied by many authors, for particular strings only. In this paper, arbitrary strings are considered. The associated generating function is evaluated when τ is a Dyck prefix (or a Dyck suffix). Furthermore, the case ...
متن کاملEnumeration of area-weighted Dyck paths with restricted height
Dyck paths are directed walks on Z starting at (0, 0) and ending on the line y = 0, which have no vertices with negative y-coordinates, and which have steps in the (1, 1) and (1,−1) directions [11]. We impose the additional geometrical constraint that the paths have height at most h, that is, they lie between lines y = 0 and y = h. Given a Dyck path π, we define the length n(π) to be half the n...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1999
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(98)00371-9