16 citations · 29 across the 10 of their papers we have counts for
10 papers
Interactions between Ehrenfest's urns arising from group actions
Hiroshi Mizukawa
Ehrenfest's diffusion model is a well-known classical physical model consisting of two urns and n balls. A group theoretical interpretation of the model by using the Gelfand pair (…
Glaisher combinatorics of regular partitions
Hiroshi Mizukawa, Hiro-Fumi Yamada
Extending the notion of -(class) regular partitions, we define -class regular partitions. A partition identity is presented and described by making use of the…
Schur function identities arising from the basic representation of
Hiroshi Mizukawa, Tatsuhiro Nakajima, Ryoji Seno +1
A Lie theoretic interpretation is given for some formulas of Schur functions and Schur -functions. Two realizations of the basic representation of the Lie algebra ar…
Finite Gelfand Pair Approaches for Ehrenfest Diffusion Model
Hiroshi Mizukawa
A classical diffusion model of Ehrenfest which consists of -urns and -balls is realized by a finite Gelfand pair , where is the hyperoctahedral group a…
Orthogonality Relations for Multivariate Krawtchouk Polynomials
Hiroshi Mizukawa
The orthogonality relations of multivariate Krawtchouk polynomials are discussed. In case of two variables, the necessary and sufficient conditions of orthogonality is given by Grü…
Wreath Product Generalizations of the Triple and Their Spherical Functions
Hiroshi Mizukawa
The symmetric group and the hyperoctaheadral group is a Gelfand triple for an arbitrary linear representation of . Their -spherical functions can be…