NAME: Christian Krattenthaler

ADDRESS: Institut f\"ur Mathematik
         Universit\"at Wien
         Strudlhofgasse 4
         A-1090 Vienna
         AUSTRIA

EMAIL ADDRESS: kratt@pap.univie.ac.at

TITLE OF TALK: Variations of a determinant by Andrews and enumeration
               of plane partitions and rhombus tilings

ABSTRACT OF TALK: 

The "stars" of my talk will be the determinants
$$ 
\det_{0\le i,j\le n} ( \omega \delta_{ij} + \binom {m+i+j} {j} ), 
$$
where $\omega$ is any sixth root of unity.
When $\omega=1$ this is a famous determinant: It was evaluated by
George Andrews thus proving the (at that time) conjectured formula for
the number of cyclically symmetric plane partitions.
In my talk, I will explain the combinatorial significance of these
determinants. They arise in enumeration problems on plane partitions
posed by Stembridge and in the enumeration of rhombus tilings of a
hexagon with a triangle removed from its centre. 
I will demonstrate how these determinants can be evaluated, thus
solving the aforementioned enumeration problems.

 
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