Tag Archives: matching

A combinatorial proof: PIE a la mode!

Continuing from my last post in this series, we’re trying to show that , where is defined as which is what we get when we start with a sequence of consecutive th powers and repeatedly take successive differences. Recall that … Continue reading

Posted in arithmetic, combinatorics, proof | Tagged , , , , , | Leave a comment

A combinatorial proof: counting bad functions

In a previous post we derived the following expression: . We are trying to show that , in order to show that starting with a sequence of consecutive th powers and repeatedly taking successive differences will always result in . … Continue reading

Posted in arithmetic, combinatorics, proof | Tagged , , , , , | 1 Comment

A combinatorial proof: functions and matchings

We’re trying to prove the following equality (see my previous post for a recap of the story so far): In particular we’re trying to show that the two sides of this equation correspond to two different ways to count the … Continue reading

Posted in arithmetic, combinatorics, proof | Tagged , , , , , | 5 Comments

Making our equation count

[This is post #4 in a series; previous posts can be found here: Differences of powers of consecutive integers, Differences of powers of consecutive integers, part II, Combinatorial proofs.] We’re still trying to find a proof of the equation which … Continue reading

Posted in combinatorics, pictures | Tagged , , , , | 3 Comments