Combinatorial multinomial matrices and multinomial Stirling numbers

Author:
Daniel S. Moak

Journal:
Proc. Amer. Math. Soc. **108** (1990), 1-8

MSC:
Primary 05A10; Secondary 15A15, 39B60, 92A15

DOI:
https://doi.org/10.1090/S0002-9939-1990-0965944-4

MathSciNet review:
965944

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Abstract | References | Similar Articles | Additional Information

Abstract: Fred C. Barnett and James R. Weaver considered the stochastic matrix (1)

These matrices also appear in a different context when Konrad J. Heuvers, et al, studied the characterization of the permanent function by the Cauchy-Binet formula. In this paper, the eigenvalues and inverse of the matrix (2) are given and the existence of a basis of right eigenvectors is established.

In the process the inverse of a generalized multinomial coefficient matrix is found.

**[1]**F. C. Barnett and J. R. Weaver,*Eigenvalues and eigenvectors of a certain stochastic matrix*, Linear and Multilinear Algebra**13**(1983), 345-350. MR**704783 (84k:15010a)****[2]**D. A. Cohen,*Basic techniques of combinatorial theory*, John Wiley and Sons, Inc., New York, 1978. MR**533589 (81i:05001)****[3]**K. J. Heuvers, L. J. Cummings and K. P. S. Bhaskara Rao,*A characterization of the permanent function by the Binet-Cauchy Theorem*, Linear Algebra Appl.**101**(1988), 49-72. MR**941295 (89h:15013)****[4]**J. Riordan,*Combinatorial identities*, John Wiley and Sons, Inc., New York, 1968. MR**0231725 (38:53)****[5]**R. Shelton, K. J. Heuvers, K. P. S. Bhaskara Rao and D. S. Moak,*Multinomial matrices*, Discrete Math.**61**(1986), 107-114. MR**850935 (87g:15009)**

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DOI:
https://doi.org/10.1090/S0002-9939-1990-0965944-4

Article copyright:
© Copyright 1990
American Mathematical Society