منابع مشابه
Lattice 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 کاملCounting Lattice Paths by Narayana Polynomials
Let d(n) count the lattice paths from (0, 0) to (n, n) using the steps (0,1), (1,0), and (1,1). Let e(n) count the lattice paths from (0, 0) to (n, n) with permitted steps from the step set N × N − {(0, 0)}, where N denotes the nonnegative integers. We give a bijective proof of the identity e(n) = 2n−1d(n) for n ≥ 1. In giving perspective for our proof, we consider bijections between sets of la...
متن کاملPolynomials, Meanders, and Paths in the Lattice of Noncrossing Partitions
For every polynomial f of degree n with no double roots, there is an associated family C(f) of harmonic algebraic curves, fibred over the circle, with at most n−1 singular fibres. We study the combinatorial topology of C(f) in the generic case when there are exactly n − 1 singular fibres. In this case, the topology of C(f) is determined by the data of an n-tuple of noncrossing matchings on the ...
متن کاملLattice paths and the quadratic coefficient of Kazhdan-Lusztig polynomials
In 1979, Kazhdan and Lusztig defined a family Pu,v(q) of polynomials indexed by pairs of elements of a Coxeter group W that have proven to be fundamental objects of study in representation theory. At the same time, they can be defined combinatorially, and so have also been studied by combinatorialists. Although it is now known that Pu,v(q) depends only on the structure of the Bruhat interval [u...
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: Advances in Applied Mathematics
سال: 2017
ISSN: 0196-8858
DOI: 10.1016/j.aam.2017.01.003