Tag Archives: binomial coefficients

Making our equation count

Posted on March 3, 2012 by Brent

[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

Combinatorial proofs

Posted on February 17, 2012 by Brent

Continuing from a previous post, we found that if we begin with th powers of consecutive integers and then repeatedly take successive differences, it seems like we always end up with the factorial of , that is, . We then … Continue reading →

Posted in combinatorics, pictures, proof | Tagged , , | 12 Comments

Differences of powers of consecutive integers, part II

Posted on February 16, 2012 by Brent

If you spent some time playing around with the procedure from Differences of powers of consecutive integers (namely, raise consecutive integers to the th power, and repeatedly take pairwise differences until reaching a single number) you probably noticed the curious … Continue reading →

Posted in arithmetic, iteration, pascal's triangle | Tagged , , , , | 3 Comments

Some words about Post without words #2

Posted on September 11, 2011 by Brent

My previous post displayed this picture: As Yuriy Kashnikov guessed, I made this picture using diagrams, a Haskell library I am developing for creating images like this. (You can see the source code for this picture here.) If you haven’t … Continue reading →

Posted in counting, pascal's triangle, pattern, pictures | Tagged , , , , | 4 Comments

Distributing cookies: solutions

Posted on April 14, 2009 by Brent

And now for some solutions to the cookie distribution problem. I’m actually going to describe four different methods of solution, and thereby (re)discover some nice combinatorial identities along the way. This is what I love about combinatorics—you discover all this … Continue reading →

Posted in counting, proof, solutions | Tagged , , , , , | 4 Comments