p-rook numbers and cycle counting in the wreath product of Cp and Sn
Meesue Yoo (유미수)
School of Mathematics, KIAS, Seoul, Korea
School of Mathematics, KIAS, Seoul, Korea
2012/4/4 Wed 4PM-5PM
The cycle counting rook numbers, hit numbers, and q-rook numberes and q-hit numbers have been studied by many people, and Briggs and Remmel introduced the theory of p-rook and p-hit numbers which is a rook theory model of the weath product of the cyclic group Cp and the symmetric group Sn.
We extend the cycle-counting q-rook numberes and q-hit numbers to the Briggs-Remmel model. In such a settinig, we define multivariable version of the cycle-counting q-rook numbers and cycle-counting q-hit numbers where we keep track of cycles of pernutation and partial permutation of Cp wearth product with Sn according to the signs of the cycles.
This work is a joint work with Jim Haglund at University of Pennsylvania and Jeff Remmel at UCSD.
We extend the cycle-counting q-rook numberes and q-hit numbers to the Briggs-Remmel model. In such a settinig, we define multivariable version of the cycle-counting q-rook numbers and cycle-counting q-hit numbers where we keep track of cycles of pernutation and partial permutation of Cp wearth product with Sn according to the signs of the cycles.
This work is a joint work with Jim Haglund at University of Pennsylvania and Jeff Remmel at UCSD.