Some strings in Dyck paths
نویسندگان
چکیده
منابع مشابه
General 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 کاملStrings of Length 3 in Grand-Dyck Paths and the Chung-Feller Property
This paper deals with the enumeration of Grand-Dyck paths according to the statistic “number of occurrences of τ” for every string τ of length 3, taking into account the number of flaws of the path. Consequently, some new refinements of the Chung-Feller theorem are obtained.
متن کاملEuler Coefficients and Restricted Dyck Paths
One of the most recent papers on patterns occurring k times in Dyck paths was written by A. Sapounakis, I. Tasoulas, P. Tsikouras, Counting strings in Dyck paths, 2007, to appear in Discrete Mathematics [5]. The authors find generating functions for all 16 patterns generated by combinations of four up (ր) and down (ց) steps. A Dyck path starts at (0, 0), takes only up and down steps, and ends a...
متن کاملRecursive Generation of k-ary Trees
In this paper we present a construction of every k-ary tree using a forest of (k− 1)ary trees satisfying a particular condition. We use this method recursively for the construction of the set of k-ary trees from the set of (k−1)-Dyck paths, thus obtaining a new bijection φ between these two sets. Furthermore, we introduce a new order on [k]∗ which is used for the full description of this biject...
متن کاملThe Dyck pattern poset
We introduce the notion of pattern in the context of lattice paths, and investigate it in the specific case of Dyck paths. Similarly to the case of permutations, the pattern-containment relation defines a poset structure on the set of all Dyck paths, which we call the Dyck pattern poset. Given a Dyck path P , we determine a formula for the number of Dyck paths covered by P , as well as for the ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Australasian J. Combinatorics
دوره 39 شماره
صفحات -
تاریخ انتشار 2007