Smallest number to appear n times in Pascal's triangle
Marc LeBrun
mlb at fxpt.com
Mon Nov 22 20:15:58 CET 2004
> Do you know if the number of times a binomial coefficient greater than 1
appears is bounded?
I may be mistaken, but I think so. choose(n,k) grows like O(n^k),
right? So they will eventually exceed any given C. The first to go will
be the central column, the last to sail over the horizon will be the pair
at C=choose(C,1)=choose(C,C-1). So there's a bounded region which contains
all instances of C.
However this bound doesn't tell us exactly how many copies of C actually
occur in that corner of Pascal's triangle. It also tells us nothing about
whether or not *some* C occurs exactly five (or however many) times.
Interesting problem...
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