A bijective proof of Kadell's conjecture on plane partitions

Abstract

We give a weight-preserving bijection fromℱ ^m _{r, µ} to

, whereℱ ^m _{r, µ} is the set of all plane partitions whose entries are ≤m and whose entries below ther-th row form a column strict plane partition of typeμ, andℱ ^m _µ the set of all column strict plane partitions of typeμ whose entries are ≤m, and

the set of all plane partitions with at mostr rows, whose entries are ≤m. This confirms a conjecture of Kadell.