Kyungyong Lee ; Li Li
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On the diagonal ideal of (C2)n and q,t-Catalan numbers
dmtcs:2838 -
Discrete Mathematics & Theoretical Computer Science,
January 1, 2010,
DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)
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https://doi.org/10.46298/dmtcs.2838
On the diagonal ideal of (C2)n and q,t-Catalan numbersConference paper
Authors: Kyungyong Lee 1; Li Li 2
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Kyungyong Lee;Li Li
1 Department of mathematics Purdue University
2 Department of Mathematics [Urbana]
Let In be the (big) diagonal ideal of (C2)n. Haiman proved that the q,t-Catalan number is the Hilbert series of the graded vector space Mn=⨁d1,d2(Mn)d1,d2 spanned by a minimal set of generators for In. We give simple upper bounds on dim(Mn)d1,d2 in terms of partition numbers, and find all bi-degrees (d1,d2) such that dim(Mn)d1,d2 achieve the upper bounds. For such bi-degrees, we also find explicit bases for (Mn)d1,d2.