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Recent progress in algebraic combinatorics

Name: Recent progress in algebraic combinatorics
Creator: Richard P. Stanley
Keywords: Symmetric functions and generalizations, Eigenvalues, singular values, and eigenvectors, Combinatorial probability, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Grassmannians, Schubert varieties, flag manifolds, Asymptotic enumeration, 01 natural sciences, Parametrization (Chow and Hilbert schemes), Combinatorial aspects of representation theory, FOS: Mathematics

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 11 Oct 2002Embargo end date: 01 Jan 2000 English Publisher:American Mathematical Society (AMS)Journal:Bulletin of the American Mathematical Society, volume 40, pages 55-68 (issn: 0273-0979, eissn: 1088-9485,

Authors: Richard P. Stanley;

doi: 10.1090/s0273-0979-02-00966-7 , 10.48550/arxiv.math/0010218

arXiv: http://arxiv.org/abs/math/0010218

Recent progress in algebraic combinatorics

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Abstract

We survey three recent breakthroughs in algebraic combinatorics. The first is the proof by Knutson and Tao, and later Derksen and Weyman, of the saturation conjecture for Littlewood-Richardson coefficients. The second is the proof of then!n!and(n+1)n−1(n+1)^{n-1}conjectures by Haiman. The final breakthrough is the determination by Baik, Deift, and Johansson of the limiting behavior of the length of the longest increasing subsequence of a random permutation.

Related Organizations

Massachusetts Institute of Technology
United States

Keywords

Symmetric functions and generalizations, Eigenvalues, singular values, and eigenvectors, Combinatorial probability, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Grassmannians, Schubert varieties, flag manifolds, Asymptotic enumeration, Parametrization (Chow and Hilbert schemes), Combinatorial aspects of representation theory, FOS: Mathematics, Research exposition (monographs, survey articles) pertaining to combinatorics, Mathematics - Combinatorics, Combinatorics (math.CO), 05Exx

Impact byBIP!

	citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	12
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Average
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Top 10%
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average