Asymptotic properties of B-splines, Eulerian numbers and cube slicing

[摘要] In this paper, we clarify the connections among B-splines. Eulerian numbers and cube slicing. We first show that the asymptotic formula for Eulerian numbers can be considered as a special case of the asymptotic properties of B-splines. The volume of cube slicing can be considered as a value of box spline functions. Based on the connection, a very simple proof for Laplace and Polya's formulas, which were settled by probabilistic methods, is given by spline theory. Crown Copyright (C) 2011 Published by Elsevier B.V. All rights reserved.

[发布日期] 2011-10-01

[效力级别]  Proceedings Paper

[关键词] B-splines;Eulerian numbers;Cube slicing;Asymptotic approximation