HOME:
BACK: More qt-analogs

The qt-Catalan numbers

Definition of the (q,t)-Catalan numbers
Tables of q,t-Catalan numbers in postscript form
Maple programs for computing the q,t-Catalan numbers
The connection with the operator Nabla
(NEW! Sept 7, 2000): A combinatorial interpretation for this sequence

The Catalan numbers are a well known sequence with dozens of combinatorial interpretations.

References:
  1. Images of the Catalan numbers
  2. More images
  3. a short list of combinatorial interpretations
  4. A long list of combinaotial interpretations (from Richard Stanley's Enumerative Combinatorics II)
  5.  one more image

 


Displayed below are the polynomials C_{n}(q,t) for n=2 through
n=6.  For convenience, the coefficients have been arranged
into an array: the coefficient of q^{h}t^{k} appears in
in position (h,k), indexed from (0,0) at the lower left.

Same table, different combinatorial interpretation.

 
 

 

 

 

 


Adapeted from the paper:
A REMARKABLE q,t-CATALAN SEQUENCE AND q-LAGRANGE INVERSION, Adriano Garsia, Mark Haiman