Columns of Pascal's Triangle contain Simplicial Polytopic Numbers
Theorem
The columns of Pascal's triangle contain the simplicial polytopic numbers:
- Column $0$: repeated instances of number $1$
and so on.
Proof
Need to define the simplicial polytopic numbers and demonstrate that the $n$th simplicial polytopic number of dimension $m$ is $\dbinom m n$ or whatever the formula is.
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Sources
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $35$
