Combinatorial Perspectives on the Crank and Mex Partition Statistics
Combinatorial Perspectives on the Crank and Mex Partition Statistics
Several authors have recently considered the smallest positive part missing from an integer partition, known as the minimum excludant or mex. In this work, we revisit and extend connections between Dyson's crank statistics, the mex, and Frobenius symbols, with a focus on combinatorial proof techniques. One highlight is a generating …