53 citations · 123 across the 16 of their papers we have counts for
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A new generalization of binomial coefficients
Michel Lassalle
Let be a fixed parameter and some indeterminate. We give some properties of the generalized binomial coefficients inductively defined by $k/x…
Narayana polynomials and Hall-Littlewood symmetric functions
Michel Lassalle
We show that Narayana polynomials are a specialization of row Hall-Littlewood symmetric functions. Using lambda-ring calculus, we generalize to Narayana polynomials the formulas of…
Two integer sequences related to Catalan numbers
Michel Lassalle
We prove the following conjecture of Zeilberger. Denoting by the Catalan number, define inductively by $(-1)^{n-1}A_n=C_n+\sum_{j=1}^{n-1} (-1)^{j} \binom{2n-1}{2j-1} A…
An (inverse) Pieri formula for Macdonald polynomials of type C
Michel Lassalle
We give an explicit Pieri formula for Macdonald polynomials attached to the root system C_n (with equal multiplicities). By inversion we obtain an explicit expansion for two-row Ma…
Recurrence formulas for Macdonald polynomials of type A
Michel Lassalle, Michael J. Schlosser
We consider products of two Macdonald polynomials of type A, indexed by dominant weights which are respectively a multiple of the first fundamental weight and a weight having zero…
Jack polynomials and free cumulants
Michel Lassalle
We study the coefficients in the expansion of Jack polynomials in terms of power sums. We express them as polynomials in the free cumulants of the transition measure of an anisotro…
Two positivity conjectures for Kerov polynomials
Michel Lassalle
Kerov polynomials express the normalized characters of irreducible representations of the symmetric group, evaluated on a cycle, as polynomials in the free cumulants of the associa…
An explicit formula for the characters of the symmetric group
Michel Lassalle
We give an explicit expression of the normalized characters of the symmetric group in terms of the contents of the partition labelling the representation.
A positivity conjecture for Jack polynomials
Michel Lassalle
We present a positivity conjecture for the coefficients of the development of Jack polynomials in terms of power sums. This extends Stanley's ex-conjecture about normalized charact…
Some conjectures for Macdonald polynomials of type B, C, D
Michel Lassalle
We present conjectures giving formulas for the Macdonald polynomials of type B, C, D which are indexed by a multiple of the first fundamental weight. The transition matrices betwee…
Inversion of the Pieri formula for Macdonald polynomials
Michel Lassalle, Michael Schlosser
We give the explicit analytic development of Macdonald polynomials in terms of "modified complete" and elementary symmetric functions. These expansions are obtained by inverting th…
A short proof of generalized Jacobi-Trudi expansions for Macdonald polynomials
Michel Lassalle
We give an elementary proof of the development of Macdonald polynomials in terms of "modified complete" and elementary symmetric functions.
An analytic formula for Macdonald polynomials
Michel Lassalle, Michael Schlosser
We give the explicit analytic development of any Jack or Macdonald polynomial in terms of elementary (resp. modified complete) symmetric functions. These two developments are obtai…
Jack polynomials and some identities for partitions
Michel Lassalle
We prove an identity about partitions involving new combinatorial coefficients. The proof given is using a generating function. As an application we obtain the explicit expression…
A new family of positive integers
Michel Lassalle
Let n,p,k be three positive integers. We prove that the numbers binomial (n,k) 3F2 (1-k, -p, p-n ; 1, 1-n ; 1) are positive integers which generalize the classical binomial coeffic…
A conjecture about partitions
Michel Lassalle
We present a conjecture about partitions, with a very elementary formulation.