分野別セミナー

Abstract:
This is a joint work with Taizo Sadahiro (Tsuda College).
Carries process is a Markov chain of carries in adding n numbers. We consider a generalization of that, studied the transition probability matrix, and its relation to combinatorics.

The results include:
(1) the stationary distribution is proportional to the decent statistics of colored permutation group
(2) left eigenvector matrix is equal to the Foulkes character table of G(p, n)
(3) Stirling-Frobenius number appears in the right eigenvector matrix
(4) Discussion on the generalized riffle shuffles whose descent process is equally distributed to the carries process.