A regular determinant of binomial coefficients

Author:
Philip C. Tonne

Journal:
Proc. Amer. Math. Soc. **41** (1973), 17-23

MSC:
Primary 15A15

MathSciNet review:
0318178

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Abstract: Let be a positive integer and suppose that each of and is an increasing sequence of nonnegative integers. Let be the matrix such that , where is the number of combinations of objects taken at a time. We give an explicit formula for the determinant of as a sum of nonnegative quantities. Further, if , we show that the determinant of is positive.

**[1]**S. Günther,*Von der expliciten Darstelling der regulären Determinanten aus Binomialcoefficienten*, Z. Math. Phys.**24**(1879), 96-103.**[2]**Sir Thomas Muir,*Contributions to the history of determinants*, 1900-1920, Blackie and Son, London, 1930.**[3]**-,*The theory of determinants in the historical order of development*, Macmillan, London, 1923.**[4]**J. W. Neuberger,*A quasi-analyticity condition in terms of finite differences*, Proc. London Math. Soc. (3)**14**(1964), 245–259. MR**0159914**

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DOI:
https://doi.org/10.1090/S0002-9939-1973-0318178-0

Article copyright:
© Copyright 1973
American Mathematical Society