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There are good examples in the book that are used to prove Pascal's Identity and Vandermonde's Identity (pgs 366-367). It's really more about explaining the types of combinations you're considering and the number of possibilities there are rather than using algebra to manipulate numbers / equations. Sorry, I know that was a horrible explanation, but hopefully the book will help you out more. --[[User:Rhollowe|Rhollowe]] 16:56, 4 February 2009 (UTC) | There are good examples in the book that are used to prove Pascal's Identity and Vandermonde's Identity (pgs 366-367). It's really more about explaining the types of combinations you're considering and the number of possibilities there are rather than using algebra to manipulate numbers / equations. Sorry, I know that was a horrible explanation, but hopefully the book will help you out more. --[[User:Rhollowe|Rhollowe]] 16:56, 4 February 2009 (UTC) | ||
| − | In a combinatorial proof you show that you can obtain identical results, in this case, selecting certain elements from a set, in two different ways. | + | In a combinatorial proof you show that you can obtain identical results, in this case, selecting certain elements from a set, in two different ways. In this particular problem, on the left hand side, you are selecting k integers from a set of n elements to form a subset, and then picking one element from the subset of k elements. On the right hand side, you are selecting one element from a set of n elements, and then selecting k-1 elements from the remaining n-1 elements to complete the subset of k elements. Hope this helps --[[User:Jdrummon|Jdrummon]] 23:53, 4 February 2009 (UTC) |
Latest revision as of 18:54, 4 February 2009
Can someone please refresh my memory on what a 'combinatorial proof' is? I'm having trouble grasping the concept and how to apply it here. Thanks!
There are good examples in the book that are used to prove Pascal's Identity and Vandermonde's Identity (pgs 366-367). It's really more about explaining the types of combinations you're considering and the number of possibilities there are rather than using algebra to manipulate numbers / equations. Sorry, I know that was a horrible explanation, but hopefully the book will help you out more. --Rhollowe 16:56, 4 February 2009 (UTC)
In a combinatorial proof you show that you can obtain identical results, in this case, selecting certain elements from a set, in two different ways. In this particular problem, on the left hand side, you are selecting k integers from a set of n elements to form a subset, and then picking one element from the subset of k elements. On the right hand side, you are selecting one element from a set of n elements, and then selecting k-1 elements from the remaining n-1 elements to complete the subset of k elements. Hope this helps --Jdrummon 23:53, 4 February 2009 (UTC)
