A spline interpretation of Eulerian numbers

Abstract

In this paper, we explore the interrelationship between Eulerian numbers and B splines. Specifically, using B splines, we give the explicit formulas of the refined Eulerian numbers, and descents polynomials. Moreover, we prove that the coefficients of descent polynomials $D_d^n(t)$ are log-concave. This paper also provides a new approach to study Eulerian numbers and descent polynomials.

6 pages

Cited by in corpus (2)

• The asymptotic properties of Eulerian numbers and refined Eulerian numbers: A Spline perspective
• Approximation of curves with piecewise constant or piecewise linear functions