Mathematics – Combinatorics

Scientific paper

[
0.00
] – not rated yet
Voters
0
Comments 0

2009-09-09

Mathematics

Combinatorics

29 pages

Scientific paper

Let $I$ be the ideal generated by alternating polynomials in two sets of $n$ variables. Haiman proved that the $q,t$-Catalan number is the Hilbert series of the graded vector space $M(=\bigoplus_{d_1,d_2}M_{d_1,d_2})$ spanned by a minimal set of generators for $I$. In this paper we give simple upper bounds on $\text{dim}M_{d_1, d_2}$ in terms of partition numbers, and find all bi-degrees $(d_1,d_2)$ such that $\dim M_{d_1, d_2}$ achieve the upper bounds. For such bi-degrees, we also find explicit bases for $M_{d_1, d_2}$. The main idea is to define and study a nontrivial linear map from $M$ to a polynomial ring $\C[\rho_1, \rho_2,...]$.

**Lee Kyungyong**

Mathematics – Algebraic Geometry

Scientist

**Li Li**

Physics – High Energy Physics – High Energy Physics - Theory

Scientist

No associations

LandOfFree

If you have personal experience with

$q,t$-Catalan numbers and generators for the radical ideal defining the diagonal locus of $(\C^2)^n$does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.$q,t$-Catalan numbers and generators for the radical ideal defining the diagonal locus of $(\C^2)^n$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and $q,t$-Catalan numbers and generators for the radical ideal defining the diagonal locus of $(\C^2)^n$ will most certainly appreciate the feedback.

Profile ID: LFWR-SCP-O-385329

Use Google custom search:

All data on this website is collected from public sources.
Our data reflects the most accurate information available at the time of publication.