Circular Digraph Walks, $k$-Balanced Strings, Lattice Paths and Chebychev Polynomials
نویسندگان
چکیده
منابع مشابه
Circular Digraph Walks, k-Balanced Strings, Lattice Paths and Chebychev Polynomials
We count the number of walks of length n on a k-node circular digraph that cover all k nodes in two ways. The first way illustrates the transfer-matrix method. The second involves counting various classes of height-restricted lattice paths. We observe that the results also count so-called k-balanced strings of length n, generalizing a 1996 Putnam problem. Corresponding Author This work was supp...
متن کاملDigraph Polynomials for Counting Cycles and Paths
Many polynomial invariants are defined on graphs for encoding the combinatorial information and researching them algebraically. In this paper, we introduce the cycle polynomial and the path polynomial of directed graphs for counting cycles and paths, respectively. They satisfy recurrence relations with respect to elementary edge or vertex operations. They are related to other polynomials and ca...
متن کاملLattice paths and random walks
Lattice paths are ubiquitous in combinatorics and algorithmics, where they are either studied per se, or as a convenient encoding of other structures. Logically, they play an important role in Philippe’s papers. For instance, they are central in his combinatorial theory of continued fractions, to which Chapter 3 of this volume is devoted. In this chapter, we present a collection of seven papers...
متن کاملLattice Paths and Faber Polynomials
The rth Faber polynomial of the Laurent series f(t) = t + f0 + f1/t + f2/t + · · · is the unique polynomial Fr(u) of degree r in u such that Fr(f) = tr + negative powers of t. We apply Faber polynomials, which were originally used to study univalent functions, to lattice path enumeration.
متن کاملLattice Paths and Kazhdan-lusztig Polynomials
In their fundamental paper [18] Kazhdan and Lusztig defined, for every Coxeter group W , a family of polynomials, indexed by pairs of elements of W , which have become known as the Kazhdan-Lusztig polynomials of W (see, e.g., [17], Chap. 7). These polynomials are intimately related to the Bruhat order of W and to the geometry of Schubert varieties, and have proven to be of fundamental importanc...
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: The Electronic Journal of Combinatorics
سال: 2008
ISSN: 1077-8926
DOI: 10.37236/832