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The numer of
multinomial coefficients divisible by a fixed power of a
prime
Frederic Timothy Howard |
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Vol. 50 (1974), No. 1, 99–108
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Abstract |
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In this paper some results of L. Carlitz and the writer concerning the number of binomial coefficients divisible by pj but not by pj+1 are generalized to multinomial coefficients. In particular 𝜃j(k;n) is defined to be the number of multinomial coefficients n|[n1,⋯,nk] divisible by exactly pj, and formulas are found for 𝜃j(k;n) for certain values of j and n. Also the generating function technique used by Carlitz for binomial coefficients is generalized to multinomial coefficients. |
Mathematical Subject Classification 2000
Primary: 10A25
Secondary: 05A10
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Milestones
Received: 11 September 1972
Published: 1 January 1974
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Authors |
| Frederic Timothy Howard | |
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