Lattice path encodings in a combinatorial proof of a differential identity

被引：3

作者：

Varvak, Anna ^{[1
]}

机构：

[1] Soka Univ Amer, Aliso Viejo, CA 92656 USA

来源：

DISCRETE MATHEMATICS | 2008年 / 308卷 / 23期

关键词：

Lattice paths; Motzkin paths; Lukasiewicz paths; Differential operators;

D O I：

10.1016/j.disc.2007.10.020

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We specify procedures by which Lukasiewicz paths can encode combinatorial objects, such as involutions, partitions, and permutations. As application, We use these encoding procedures to give a combinatorial proof of the differential operator identity exp (y(d/dx + f(x))) = exp (integral(y)(0) f(t + x)dt) exp (y d/dx). due to Stanley. Taylor's theorem is a special case of this differential identity where f (x) = 0. (C) 2007 Elsevier B.V. All rights reserved.

引用

页码：5834 / 5840

页数：7