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Generalized carries process and riffle shuffles

Hold Date
2016-08-26 16:30〜2016-08-26 18:00
Seminar Room W1-D-610, West Zone 1, Ito campus, Kyushu University
Object person
Fumihiko NAKANO (Gakushuin University)

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.