Characteristic and Ehrhart Polynomials
Journal of Algebraic Combinatorics: An International Journal
Lagrange Inversion and Schur Functions
Journal of Algebraic Combinatorics: An International Journal
Specializations of MacMahon symmetric functions and the polynomial algebra
Discrete Mathematics
Enumeration of (p, q)-parking functions
Discrete Mathematics
A proof of the q, t-Catalan positivity conjecture
Discrete Mathematics
Short antichains in root systems, semi-Catalan arrangements, and B-stable subspaces
European Journal of Combinatorics
Proof of a monotonicity conjecture
Journal of Combinatorial Theory Series A
Journal of Combinatorial Theory Series A
Journal of Algebraic Combinatorics: An International Journal
q,t-Fuβ---Catalan numbers for finite reflection groups
Journal of Algebraic Combinatorics: An International Journal
A bijection between dominant Shi regions and core partitions
European Journal of Combinatorics
European Journal of Combinatorics
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We formulate a series of conjectures (and a few theorems) on the quotient of the polynomial ring {\Bbb Q}[x_1,\ldots , x_n, y_1, \ldots , y_n] in two sets of variables by the ideal generated by all Sn invariant polynomials without constant term. The theory of the corresponding ring in a single set of variables X = {x1, …, xn} is classical. Introducing the second set of variables leads to a ring about which little is yet understood, but for which there is strong evidence of deep connections with many fundamental results of enumerative combinatorics, as well as with algebraic geometry and Lie theory.