Adriano M. Garsia

Learn More
The lattice cell in the i + 1 st row and j + 1 st column of the positive quadrant of the plane is denoted (i; j). If is a partition of n + 1, we denote by =ij the diagram obtained by removing the cell (i; j) from the (French) Ferrers diagram of. We set =ij = det k x pj i y qj i k n i;j=1 , where (p 1 ; q 1); : : :; (p n ; q n) are the cells of =ij, and let(More)
We present here a proof that a certain rational function C n (q, t) which has come to be known as the " q, t-Catalan " is in fact a polynomial with positive integer coefficients. This has been an open problem since 1994. The precise form of the conjecture is given in the J. where it is further conjectured that C n (q, t) is the Hilbert Series of the(More)
We outline here a proof that a certain rational function C(n)(q, t), which has come to be known as the "q, t-Catalan," is in fact a polynomial with positive integer coefficients. This has been an open problem since 1994. Because C(n)(q, t) evaluates to the Catalan number at t = q = 1, it has also been an open problem to find a pair of statistics a, b on the(More)
This work is gratefully dedicated to Dominique Foata for his inspiring and pioneering work in algebraic combinatorics. We hope that he will nd it to be in harmony with the Lotharingian spirit which he has nurtured for so many years. ABSTRACT. We construct for each`n a bigraded S n-module H and conjecture that its Frobenius characteristic C (x; q; t) yields(More)
Astract We study here the ring QS n of Quasi-Symmetric Functions in the variables x 1 , x 2 ,. .. , x n. F. Bergeron and C. Reutenauer [4] formulated a number of conjectures about this ring, in particular they conjectured that it is free over the ring Λ n of symmetric functions in x 1 , x 2 ,. .. , x n. We present here an algorithm that recursively(More)