Multinomial coefficients modulo a prime

Multinomial coefficients modulo a prime

We say that the multinomial coefficient (m.c.) (j_1,\dots, j_l)=n!/ (j_1!\cdots j_l!) has order l and power n=j_1+\cdots+j_l. Let G(n,l,p) be the number of m.c. that are not divisible by p and have order l with powers which are not larger than n. If \theta =\log_p(l,p-1) and [ q_{l,p}^{(r)}=\min_{p^...

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Bibliographische Detailangaben
Veröffentlicht in:Proceedings of the American Mathematical Society 1999-02, Vol.127 (2), p.349-353
1. Verfasser: Volodin, Nikolai A.
Format: Artikel
Sprache:eng
Schlagworte:
Approximation
Binomial coefficients
Coefficients
Functions (Mathematics)
Integers
Mathematical theorems
Multinomial models
Prime numbers
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Zusammenfassung:We say that the multinomial coefficient (m.c.) (j_1,\dots, j_l)=n!/ (j_1!\cdots j_l!) has order l and power n=j_1+\cdots+j_l. Let G(n,l,p) be the number of m.c. that are not divisible by p and have order l with powers which are not larger than n. If \theta =\log_p(l,p-1) and [ q_{l,p}^{(r)}=\min_{p^r\le n
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-99-05079-0