1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Generating function model

  1. Sep 28, 2015 #1
    1. The problem statement, all variables and given/known data

    given one each of u types of candy, two each of v types of candy, and three each of of w types of candy, find a generating function for the number of ways to select r candies.



    3. The attempt at a solution

    I am not sure if I understand this correctly, but this is what I came up with

    (x^0 + x^1)^u (x^0 + x^1 + x^2)^v (x^0 + x^1 + x^2 + x^3)^w
     
  2. jcsd
  3. Sep 28, 2015 #2

    andrewkirk

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    What do you mean by a 'generating function'? Is it a probability generating function? If so, what is the random variable to which the function is being related?

    If it's not a prob-gen function, then what does the 'x' in the above equation represent?

    I'm pretty sure that, whatever the intended meaning of your expression, it won't be the answer, as it doesn't use r.

    Regarding the meaning of the question itself, I think it's clear enough. Say the candy is arranged in u+v+w cups in a line in front of you. The first u cups each have one candy in, the next v cups have two each and the last w have three each. The candies in the k-th cup all have the number k written on them. You choose r candies from the cups and thus end up with a bunch of r numbers, some of which may be the same. The question is how many different collections of numbers can you get?

    Although the question is clear, solving it doesn't seem easy. The answer will be an expression in terms of u, v, w and r. I imagine there's a standard distribution for this sort of thing. I thought maybe hypergeometric, but on a quick consideration, it didn't seem to fit. I can write it as a rather long, messy expression with multiple nested sums. There may be a slicker way though.
     
  4. Sep 28, 2015 #3
    It is not a probability generating function. This for a combinatorics class. The chapter is called "generating function models" and for this question we don't have to solve the problem, we only have to model it with a "generating function". The reason r is not included in the problem is because the answer would be the number of the coefficient of x^r when the expression is multiplied out (I am pretty sure)
     
  5. Sep 28, 2015 #4

    andrewkirk

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    I see. Well in that case your solution is correct!
     
  6. Sep 29, 2015 #5
    I find this chapter to be very abstract and confusing :/
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Generating function model
  1. Generating functions (Replies: 2)

  2. Generating Functions (Replies: 0)

  3. Generating Function (Replies: 0)

  4. Generating Function (Replies: 3)

  5. Generating Function (Replies: 4)

Loading...