2,603 research outputs found
A Combinatorial Formula for Macdonald Polynomials
We prove a combinatorial formula for the Macdonald polynomial H_mu(x;q,t)
which had been conjectured by the first author. Corollaries to our main theorem
include the expansion of H_mu(x;q,t) in terms of LLT polynomials, a new proof
of the charge formula of Lascoux and Schutzenberger for Hall-Littlewood
polynomials, a new proof of Knop and Sahi's combinatorial formula for Jack
polynomials as well as a lifting of their formula to integral form Macdonald
polynomials, and a new combinatorial rule for the Kostka-Macdonald coefficients
K_{lambda,mu}(q,t) in the case that mu is a partition with parts less than or
equal to 2.Comment: 29 page
Some combinatorial identities related to commuting varieties and Hilbert schemes
In this article we explore some of the combinatorial consequences of recent results relating the isospectral commuting variety and the Hilbert scheme of points in the plane
A smoother end to the dark ages
Independent lines of evidence suggest that the first stars, which ended the
cosmic dark ages, came in pairs, rather than singly. This could change the
prevailing view that the early Universe had a Swiss-cheese-like appearance.Comment: Nature News and Views, April 7, 201
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