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Re^3: Combinatorics problem. (Updated with more info.)

by danaj (Friar)
on Dec 11, 2015 at 23:06 UTC ( [id://1150081] : note . print w/replies, xml ) Need Help??


in reply to Re^2: Combinatorics problem. (Updated with more info.)
in thread Combinatorics problem. (Updated with more info.)

From DLMF or MathWorld we see the number of restricted compositions is binomial(n-1,m-1). So:

perl -Mntheory=:all -E 'say binomial(12-1,7-1)' 462

Basically the same with Math::Pari or Pari/GP.

Chinn and Heubach (2003) and Opdyke (2008) have interesting info relating restricted compositions to Pascal's triangle.

Edit: There's also some interesting but scattered info on OEISWiki, including the idea of encoding the compositions as RLE on binary. For generating the sequences, Kelleher's paper is a great reference.