Beefy Boxes and Bandwidth Generously Provided by pair Networks
Your skill will accomplish
what the force of many cannot

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

by danaj (Friar)
on Dec 11, 2015 at 23:06 UTC ( #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.

Log In?

What's my password?
Create A New User
Domain Nodelet?
Node Status?
node history
Node Type: note [id://1150081]
and the web crawler heard nothing...

How do I use this? | Other CB clients
Other Users?
Others meditating upon the Monastery: (4)
As of 2022-01-17 01:36 GMT
Find Nodes?
    Voting Booth?
    In 2022, my preferred method to securely store passwords is:

    Results (50 votes). Check out past polls.