On a Function Related to Multinomial Coefficients (I) |
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| Authors: | Yong Gao Chen Chun Gang Ji |
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| Affiliation: | (1) Department of Mathematics, Nanjing Normal University, Nanjing 210097, P. R. China E-mail: ygchen@pine.njnu.edu.cn, CN;(2) Department of Mathematics, Nanjing Normal University, Nanjing 210097, P. R. China and Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, P. R. China E-mail: cgji@amss.ac.cn, CN |
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| Abstract: | Let F p,t (n) denote the number of the coefficients of (x 1+1x 2+...+x t ) j , 0 ≤j≤n− 1, which are not divisible by the prime p. Define G p,t (n) = F p,t /n θ and β(p,t) = lim infF p,t )(n)/n θ, where θ = (log)/(log p). In this paper, we mainly prove that G p,t can be extended to a continuous function on ℝ+, and the function G p,t is nowhere monotonic. Both the set of differential points of the function G p,t and the set of non-differential points of the function G p,t are dense in ℝ+. Received February 18, 2000, Accepted December 7, 2000 |
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| Keywords: | Prime numbers Multinomial coefficients Function |
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