4 papers · 1 filter
A descent-excedance correspondence in colored permutation groups
Hiranya Kishore Dey, Umesh Shankar, Sivaramakrishnan Sivasubramanian
It is well known that descents and excedances are equidistributed in the symmetric group. We show that the descent and excedance enumerators, summed over permutations with a fixed…
Two bijections in the spirit of the transformation fondamentale
Umesh Shankar
In this short paper, we give bijective proofs of two recent equidistribution results connecting cyclic and linear statistics in the spirit of the Foata's ``transformation fondament…
Synchronicity of descent and excedance enumerators in the alternating subgroup
Umesh Shankar
Generalising the work of Dey, we define the notion of ultra-synchronicity of sequences of real numbers. Let be the number of even permutations wit…
Canonical reduced words and signed descent length enumeration in Coxeter groups
Umesh Shankar, Sivaramakrishnan Sivasubramanian
Reifegerste and independently, Petersen and Tenner studied a statistic on permutations in . Two other studied statistics on are…