Interpolating Set Partition Statistics

Abstract Four statistics on set partitions were introduced by Wachs and White. These statistics had q -Stirling numbers as their distribution generating function. The distribution of these statistics on non-crossing statistics was investigated by Simion. We introduce classes of statistics which interpolate between pairs of these four statistics. We give sufficient conditions for these classes to be q -Stirling distributed. We describe the restriction of these classes to non-crossing statistics. We also describe an interpolating statistic between the set partition major index of Sagan and its “hard” analog.