Symmetric functions. (Fonctions symétriques.)
Symmetric functions for the generating matrix of the Yangian of .
Symmetric monoidal completions and the exponential principle among labeled combinatorial structures.
Symmetric polynomials and divided differences in formulas of intersection theory
The goal of this paper is at least two-fold. First we attempt to give a survey of some recent (and developed up to the time of the Banach Center workshop Parameter Spaces, February '94) applications of the theory of symmetric polynomials and divided differences to intersection theory. Secondly, taking this opportunity, we complement the story by either presenting some new proofs of older results (and this takes place usually in the Appendices to the present paper) or providing some new results which...
Tableau cycling and Catalan numbers.
Tableaux in the Whitney module of a matroid.
Tensor Products and Dimensions of simple Modules for Symmetric Groups.
Tensorial square of the hyperoctahedral group coinvariant space.
The 6 vertex model and Schubert polynomials.
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 Apollonian decay of beer foam bubble size distribution and the lattices of Young diagrams and their correlated mixing functions.
The asymptotic behavior of elementary symmetric functions on a probability distribution.
The centers of gravity of the associahedron and of the permutahedron are the same.
The cleanness of (symbolic) powers of Stanley-Reisner ideals
Let be a pure simplicial complex on the vertex set and its Stanley-Reisner ideal in the polynomial ring . We show that is a matroid (complete intersection) if and only if () is clean for all and this is equivalent to saying that (, respectively) is Cohen-Macaulay for all . By this result, we show that there exists a monomial ideal with (pretty) cleanness property while or is not (pretty) clean for all integer . If , we also prove that () is clean if and only if (,...
The combinatorial structure of trigonometry.
The combinatorics of Macdonald's operator.
The combinatorics of orbital varieties closures of nilpotent order 2 in .
The combinatorics of quiver representations
We give a description of faces, of all codimensions, for the cones spanned by the set of weights associated to the rings of semi-invariants of quivers. For a triple flag quiver and its faces of codimension 1 this description reduces to the result of Knutson-Tao-Woodward on the facets of the Klyachko cone. We give new applications to Littlewood-Richardson coefficients, including a product formula for LR-coefficients corresponding to triples of partitions lying on a wall of the Klyachko cone. We systematically...
The combinatorics of the Garsia-Haiman modules for hook shapes.
The difference matrices of the classes of a Sharma-Kaushik partition
Sharma-Kaushik partitions have been used to define distances between vectors with -coordinates. In this paper, “difference matrices” for the partitioning classes have been introduced and investigated. It has been shown that the difference matrices are circulant and that the entries of a product of matrices is an extended intersection number of a distance scheme. The sum of the entries of each row or columns of the product matrix has been obtained. The algebra of matrices generated by the difference...