Lattice Paths and Faber Polynomials

نویسندگان

  • Ira M. Gessel
  • Sangwook Ree
چکیده

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.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The hitting time subgroup, Lukasiewicz paths and Faber polynomials

This talk connects simple lattice path enumeration with a subgroup of the Riordan group, ordered trees, and the Faber polynomials from classical complex analysis. The main tools employed are matrix multiplication, generating functions and a few definitions from group theory and complex functions.

متن کامل

Coefficient Estimates for a General Subclass of m-fold Symmetric Bi-univalent Functions by Using Faber Polynomials

In the present paper, we introduce a new subclass H∑m (λ,β)of the m-fold symmetric bi-univalent functions. Also, we find the estimates of the Taylor-Maclaurin initial coefficients |am+1| , |a2m+1| and general coefficients |amk+1| (k ≥ 2) for functions in this new subclass. The results presented in this paper would generalize and improve some recent works of several earlier authors.

متن کامل

Combinatorics of Dispersionless Integrable Systems and Universality in Random Matrix Theory

It is well-known that the partition function of the unitary ensembles of random matrices is given by a τ -function of the Toda lattice hierarchy and those of the orthogonal and symplectic ensembles are τ -functions of the Pfaff lattice hierarchy. In these cases the asymptotic expansions of the free energies given by the logarithm of the partition functions lead to the dispersionless (i.e. conti...

متن کامل

A Faber Series Approach to Cardinal Interpolation

For a compactly supported function <p in Rd we study quasiinterpolants based on point evaluations at the integer lattice. We restrict ourselves to the case where the coefficient sequence Xf, for given data /, is computed by applying a univariate polynomial q to the sequence <p\Zd , and then convolving with the data f\Z(¡ . Such operators appear in the well-known Neumann series formulation of qu...

متن کامل

Counting 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 کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1996