Bivariate Gonarov polynomials and integer sequences uri icon

abstract

  • Univariate Gonarov polynomials arose from the Gonarov interpolation problem in numerical analysis. They provide a natural basis of polynomials for working with u-parking functions, which are integer sequences whose order statistics are bounded by a given sequence u. In this paper, we study multivariate Gonarov polynomials, which form a basis of solutions for multivariate Gonarov interpolation problem. We present algebraic and analytic properties of multivariate Gonarov polynomials and establish a combinatorial relation with integer sequences. Explicitly, we prove that multivariate Gonarov polynomials enumerate k-tuples of integers sequences whose order statistics are bounded by certain weights along lattice paths in k. It leads to a higher-dimensional generalization of parking functions, for which many enumerative results can be derived from the theory of multivariate Gonarov polynomials. 2014 Science China Press and Springer-Verlag Berlin Heidelberg.

published proceedings

  • Science China Mathematics

author list (cited authors)

  • Khare, N., Lorentz, R., & Yan, C. H.

citation count

  • 6

complete list of authors

  • Khare, Niraj||Lorentz, Rudolph||Yan, Catherine Huafei

publication date

  • August 2014