Limits of areas under lattice paths

被引:10
作者
Drake, Brian [1 ]
机构
[1] Brandeis Univ, Dept Math, Waltham, MA 02454 USA
关键词
Schroder paths; Motzkin paths; Generalized Frobenius partitions; NUMBERS;
D O I
10.1016/j.disc.2008.11.020
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We consider sequences of polynomials which count lattice paths by area. In some cases the reversed polynomials approach a formal power series as the length of the paths tend to infinity. We find the limiting series for generalized Schroder, Motzkin, and Catalan paths. The limiting series for Schroder paths and their generalizations are shown to count partitions with restrictions on the multiplicities of odd parts and no restrictions on even parts. The limiting series for generalized Motzkin and Catalan paths are shown to count generalized Frobenius partitions and some related arrays. (C) 2008 Elsevier B.V. All rights reserved.
引用
收藏
页码:3936 / 3953
页数:18
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