q-Analogs of the inclusion–exclusion principle
and permutations with restricted position

William Y. C. Chen and Gian–Carlo Rota

  Abstract:  We derive a q-analog of the principle of inclusion–exclusion, and use it to derive a q-analog of the Kaplansky–Riordan theory of permutations with restricted position. Some analogs with the theory of Mahonian statistics are pointed out at the end, leading to a conjectured relationship between the two.