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From: nmg@c3.c3.lanl.gov (Niall Graham)
Newsgroups: comp.theory
Subject: Re: Re:partitioning problem
Message-ID: <NMG.90Dec2205731@c3.c3.lanl.gov>
Date: 3 Dec 90 03:57:31 GMT
References: <58269@brunix.UUCP>
Sender: news@lanl.gov
Organization: Los Alamos National Laboratory, New Mexico
Lines: 28
In-reply-to: wcn@cs.brown.edu's message of 2 Dec 90 17:10:36 GMT


Wen-Chun Ni writes:

>If I do not misinterpret your problem, the problem is in fact
>easier than the original one. No recurrence is required, and
>the answer is k^n/k!.

Oops!   k^n/k! is not an integer for k >= 3.

.
.
>Somebody (I deleted it from my file) answered this question by posing 
>an incorret answer: sum(for i=1 to k) S(n,i). 
	 
I did! And I still believe it is correct. 

Since you like generating functions I'll add that the special case
k=n yields the Bell numbers whose exponential generating function
is e^(e^x - 1)  [Ref. An old "Monthly" article by Rota].

>  Wen-Chun Ni: Department of Computer Science   
>	       Brown University,               (H) (401) 2723615
>	       Providence, RI 02912            (O) (401) 8637668
>  ________________________________________________________________


Niall Graham                    "If this is Heaven, I'm bailin' out"
Los Alamos, New Mexico                             The Birthday Party


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