The Conjugate Trace and Trace of a Plane Partition

The conjugate traceand traceof a planepartition aredefined,and thegenerating function for the number of plane partitions TT of n with <r rows and largest part <m, with conjugate trace t (or trace I, when m = co), is found. Various properties of this generating function are studied. One consequence of these properties is a formula which can be regarded as a q-analog of a well-known result arising in the representation theory of the symmetric group.