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Kyungyong Lee ; Li Li - 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) - 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 ORCID2

  • 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.


Volume: DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)
Section: Proceedings
Published on: January 1, 2010
Imported on: January 31, 2017
Keywords: q,t-Catalan number,diagonal ideal,[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
Funding:
    Source : OpenAIRE Graph
  • Commutative Algebra of Alternating Polynomials; Funder: National Science Foundation; Code: 0901367

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