On the Generating Function for Intervals in Young's Lattice

Electronic Journal of Combinatorics

article

Faqruddin Ali Azam¹  Edward Richmond² 

[1] Oklahoma State University;Department of Mathematics Oklahoma State University Oklahoma

DOI  :  10.37236/11407

学科分类：统计和概率

来源: Electronic Journal Of Combinatorics

【 摘 要 】

In this paper, we study a family of generating functions whose coefficients are polynomials that enumerate partitions in lower order ideals of Young's lattice. Our main result is that this family satisfies a rational recursion and are therefore rational functions. As an application, we calculate the asymptotic behavior of the cardinality of a lower order ideals for the "average" partition of fixed length and give a homological interpretation of this result in relation to Grassmannians and their Schubert varieties.

【 授权许可】

CC BY