Adriano M. Garsia

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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)