Biomedical subjects

M Haiman

Publications and source records attributed to M Haiman.

3 recordsLinked to original sources

PubMed2005

Combinatorial theory of Macdonald polynomials I: proof of Haglund's formula.

Haglund recently proposed a combinatorial interpretation of the modified Macdonald polynomials H(mu). We give a combinatorial proof of this conjecture, which establishes the existence and integrality of H(mu). As corollaries, we obtain the cocharge formula of Lascoux and Schutzenberger for Hall-Littlewood polynomials, a formula of Sahi and Knop for Jack's symmetric functions, a generalization of this result to the integral Macdonald polynomials J(mu), a formula for H(mu) in terms of Lascoux-Leclerc-Thibon polynomials, and combinatorial expressions for the Kostka-Macdonald coefficients K(lambda,mu) when mu is a two-column shape.

Journal Article↗

PubMed1993

A graded representation model for Macdonald's polynomials.

We define doubly graded Sn modules Rmu for which we conjecture that the multiplicities of irreducible representations in various bi-degrees are given by the Macdonald coefficients Klambdamu. Assuming one fundamental conjecture, the modules Rmu can be given several equivalent definitions, which we discuss. We prove the conjectures in various special cases.

Journal Article↗

PubMedDate not supplied

[Treatment of pseudarthroses of the olecranon with the anatomical hook plate].

We report the results in seven patients treated surgically for nonunion of the olecranon. Four nonunions occurred after primary treatment with tension band wiring and three nonunions occurred after open reduction internal fixation with plates and screws or lag screws only. All patients were treated with cancellous bone grafting and open reduction internal fixation using anatomical hook plates. All nonunions united within 6 months after the treatment. In all patients the range of motion of the elbow improved significantly.

Bone Plates↗