We derive a Murnaghan–Nakayama type formula for the values of unipotent characters of finite classical groups on regular semisimple elements. This relies on Asai’s explicit decomposition of Lusztig restriction. We use our formula to show that most complex irreducible characters vanish on some -singular element for certain primes . As an application we classify the simple endotrivial modules of ...

De Vrijer has presented a proof of the finite developments theorem which, in addition to showing that all developments are finite, gives an effective reduction strategy computing longest developments as well as a simple formula computing their length. We show that by applying a rather simple and intuitive principle of duality to de Vrijer’s approach one arrives at a proof that some developments...

The number of plane partitions contained in a given box was shown by MacMahon [8] to be given by a simple product formula. By a simple bijection, this formula also enumerates lozenge tilings of hexagons of side-lengths a, b, c, a, b, c (in cyclic order) and angles of 120 degrees. We present a generalization in the case b = c by giving simple product formulas enumerating lozenge tilings of regio...