Tensorial square of the hyperoctahedral group coinvariant space.
The adaptation of the -means algorithm to solving the multiple ellipses detection problem by using an initial approximation obtained by the DIRECT global optimization algorithm
We consider the multiple ellipses detection problem on the basis of a data points set coming from a number of ellipses in the plane not known in advance, whereby an ellipse is viewed as a Mahalanobis circle with center , radius , and some positive definite matrix . A very efficient method for solving this problem is proposed. The method uses a modification of the -means algorithm for Mahalanobis-circle centers. The initial approximation consists of the set of circles whose centers are determined...
The asymptotic behavior of elementary symmetric functions on a probability distribution.
The combinatorial structure of trigonometry.
The combinatorics of Macdonald's operator.
The hyperharmonic numbers and the phratry of the coupon collector. (Les nombres hyperharmoniques et la fratrie du collectionneur de vignettes.)
The Littlewood-Richardson rule - the cornerstone for computing group properties
The number of ribbon Schur functions.
The plethysm at hook and near-hook shapes.
The ring of multisymmetric functions
We give a presentation (in terms of generators and relations) of the ring of multisymmetric functions that holds for any commutative ring , thereby answering a classical question coming from works of F. Junker [J1, J2, J3] in the late nineteen century and then implicitly in H. Weyl book “The classical groups” [W].
The Stanley-Féray-Śniady formula for the generalized characters of the symmetric group
We show that the explicit formula of Stanley-Féray-Śniady for the characters of the symmetric group has a natural extension to the generalized characters. These are the spherical functions of the unbalanced Gel’fand pair .
The use of Schubert polynomials in SYMCHAR.
Theta functions, elliptic hypergeometric series, and Kawanaka's Macdonald polynomial conjecture.
Thom polynomials and Schur functions: the singularities
We give the Thom polynomials for the singularities associated with maps with parameter . Our computations combine the characterization of Thom polynomials via the “method of restriction equations” of Rimanyi et al. with the techniques of Schur functions.
Thom polynomials and Schur functions: the singularities
We give a closed formula for the Thom polynomials of the singularities in terms of Schur functions. Our computations combine the characterization of the Thom polynomials via the “method of restriction equations” of Rimányi et al. with the techniques of Schur functions.
Two new criteria for comparison in the Bruhat order.