Prof. J. S. Macdonald, F.R.S

The Combinatorics of Macdonald ’ S D

Abstract. To prove the existence of the Macdonald polynomials {Pλ(x; q, t)}λ`n, Macdonald [Séminaire Lotharingien Combin. 20 (1988), Article B20a; “Symmetric functions and Hall polynomials”, 2nd ed., Clarendon Press, New York, 1995] introduced an operator D n and proved that for any Schur function sλ(x1, . . . , xn), D 1 n(sλ(x1, . . . , xn)) = ∑ μ dλ,μ(q, t)sμ(x1, . . . , xn) where the sum run...

Kadell ’ s two conjectures for Macdonald polynomials

Recently Kevin Kadell found interesting properties of anti-symmetric variants of the so-called Jack polynomials [Ka]. He formulated two conjectures about negative integral and half-integral values of the parameter k (k = 1 for the characters of compact simple Lie groups). As it was observed independently by Ian Macdonald and the author, these conjectures follow readily from the interpretation o...

Prof. U. S. Nayak M.S., M.Ch., F.R.A.C.S.

Born in Vijayawada, to Dr. U.V Nayak, Professor of Anatomy at MMC, and Mrs. Sanjeevi Bai, Dr. Nayak graduated in medicine from MMC in 1954 and went on to pursue post‐graduation in general surgery from another prestigious institute, Stanley Medical College in 1959. He was the first batch pupil along with Dr. Mathangi Ramakrishnan, when the legendary Prof. C R Sunderarajan started the first M.Ch....

Prof. Dr. Prof. Prof.

6 . 042 J / 18 . 062 J , Fall ’ 05 : Mathematics for Computer Science October 3 Prof . Albert

A 1994 University of Chicago study entitled The Social Organization of Sexuality found that on average men have 74% more opposite­gender partners than women, confirming a view that men are more promiscuous. But whoever reported this finding was lying or confused! We’ll show you how to use the properties of vertex degrees in a graph to prove this. Let’s recast opposite­gender partnering in graph...