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.
@article{10_37236_11407,
author = {Faqruddin Ali Azam and Edward Richmond},
title = {On the generating function for intervals in {Young's} lattice},
journal = {The electronic journal of combinatorics},
year = {2023},
volume = {30},
number = {2},
doi = {10.37236/11407},
zbl = {1514.05010},
url = {http://geodesic.mathdoc.fr/articles/10.37236/11407/}
}
TY - JOUR
AU - Faqruddin Ali Azam
AU - Edward Richmond
TI - On the generating function for intervals in Young's lattice
JO - The electronic journal of combinatorics
PY - 2023
VL - 30
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/11407/
DO - 10.37236/11407
ID - 10_37236_11407
ER -
%0 Journal Article
%A Faqruddin Ali Azam
%A Edward Richmond
%T On the generating function for intervals in Young's lattice
%J The electronic journal of combinatorics
%D 2023
%V 30
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/11407/
%R 10.37236/11407
%F 10_37236_11407
Faqruddin Ali Azam; Edward Richmond. On the generating function for intervals in Young's lattice. The electronic journal of combinatorics, Tome 30 (2023) no. 2. doi: 10.37236/11407
