scholarly journals Generalized Binomial Coefficients for Molecular Species

2000 ◽  
Vol 91 (1-2) ◽  
pp. 15-48 ◽  
Author(s):  
Pierre Auger ◽  
Gilbert Labelle ◽  
Pierre Leroux
Keyword(s):  
Molecular Species ◽  
Binomial Coefficients ◽  
Generalized Binomial Coefficients

scholarly journals Rationality of the generalized binomial coefficients for a multiplicity free action

2000 ◽  
Vol 68 (3) ◽  
pp. 387-410 ◽  
Author(s):  
Chal Benson ◽  
Gail Ratcliff
Keyword(s):  
Vector Space ◽  
Canonical Basis ◽  
Free Action ◽  
Homogeneous Component ◽  
Binomial Coefficients ◽  
Invariant Polynomials ◽  
Finite Dimensional ◽  
Multiplicity Free ◽  
Lie Subgroup ◽  
Generalized Binomial Coefficients

AbstractLetVbe a finite dimensional Hermitian vector space andKbe a compact Lie subgroup ofU(V) for which th representation ofKonC[V] is multiplicity free. One obtains a canonical basis {pα} for the spaceC[VR]kofK-invariant polynomials on VRand also a basis {q's. The polynomialpα's yields the homogeneous component of highest degree inqα. The coefficient that express theqα's in terms of thepβ's are the generalized binomial coeffficients of Yan. The main result in this paper shows tht these numbers are rational.

scholarly journals Some Congruences for Generalized Binomial Coefficients

1995 ◽  
Vol 25 (3) ◽  
pp. 1079-1085 ◽  
Author(s):  
William A. Kimball ◽  
William A. Webb
Keyword(s):  
Binomial Coefficients ◽  
Generalized Binomial Coefficients

scholarly journals JACK POLYNOMIALS, GENERALIZED BINOMIAL COEFFICIENTS AND POLYNOMIAL SOLUTIONS OF THE GENERALIZED LAPLACE'S EQUATION

1998 ◽  
Vol 13 (09) ◽  
pp. 715-725 ◽  
Author(s):  
S. CHATURVEDI
Keyword(s):  
Homogeneous Polynomial ◽  
Binomial Coefficients ◽  
Jack Polynomials ◽  
Laplace’S Equation ◽  
Linear Combinations ◽  
Laplace's Equation ◽  
Polynomial Solutions ◽  
Sutherland Model ◽  
Generalized Binomial Coefficients

We discuss the symmetric homogeneous polynomial solutions of the generalized Laplace's equation which arises in the context of the Calogero–Sutherland model on a line. The solutions are expressed as linear combinations of Jack polynomials and the constraints on the coefficients of expansion are derived. These constraints involve generalized binomial coefficients defined through Jack polynomials. Generalized binomial coefficients for partitions of k up to k=6 are tabulated.

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