
Archives
 January 2020
 December 2019
 September 2019
 August 2019
 July 2019
 June 2019
 May 2019
 April 2019
 March 2019
 February 2019
 January 2019
 December 2018
 November 2018
 October 2018
 September 2018
 August 2018
 July 2018
 June 2018
 May 2018
 April 2018
 March 2018
 February 2018
 January 2018
 December 2017
 November 2017
 October 2017
 September 2017
 August 2017
 July 2017
 June 2017
 May 2017
 April 2017
 March 2017
 February 2017
 January 2017
 December 2016
 November 2016
 October 2016
 September 2016
 August 2016
 July 2016
 June 2016
 May 2016
 April 2016
 March 2016
 February 2016
 January 2016
 December 2015
 November 2015
 October 2015
 September 2015
 August 2015
 July 2015
 June 2015
 May 2015
 April 2015
 March 2015
 February 2015
 January 2015
 December 2014
 November 2014
 October 2014
 September 2014
 August 2014
 July 2014
 June 2014
 May 2014
 April 2014
 March 2014
 February 2014
 January 2014
 December 2013
 November 2013
 October 2013
 September 2013
 June 2013
 May 2013
 April 2013
 March 2013
 February 2013
 January 2013
 December 2012
 November 2012
 October 2012
 September 2012
 August 2012
 July 2012
 May 2012
 March 2012
 February 2012
 January 2012
 December 2011
 November 2011
 October 2011

Meta
Monthly Archives: November 2011
Another Nice Proof of the Derangements Formula
Strangely enough, a couple of days after I made my last post on a way to prove the derangements formula that I had never seen before, I came across another new (to me) way to prove the derangements formula in … Continue reading
A Nice Proof of the Derangements Formula
A derangement is a permutation in which none of the elements is mapped to itself. The formula for the number of derangements on elements is This formula is normally proved using inclusionexclusion (and, in fact, it is one of the … Continue reading
Posted in combinatorics, derangements, permutations, recurrence relations
6 Comments
A Product Calculus
The derivative can be thought of as a measure of how much changes relative to changes in . But why measure the relationship between the rates of change this way? Why not a different definition of the derivative that compares … Continue reading
Posted in calculus
2 Comments
Permutations with Fixed Points and Successions
Suppose we have a permutation on the set . A fixed point of is a value such that . If , then we say has a succession at . Take, for example, the permutation 213596784. It has four fixed points: … Continue reading
Posted in combinatorics, permutations
3 Comments
Euler Numbers via Eulerian Numbers
This is a little curiosity I discovered several years ago. The Euler numbers are the coefficients in the Maclaurin expansion of hyperbolic secant: The Eulerian numbers count the number of permutations on elements with ascents; i.e., the number of permutations … Continue reading
Posted in combinatorics
Leave a comment
Parametric Derivatives
What is the th derivative of a parametricallydefined function? For the th derivative of the product of two functions there is Leibniz’s rule, and for the th derivative of the composition of two functions there is Faà di Bruno’s formula. … Continue reading
Posted in calculus, special functions
Leave a comment
Binomial Coefficient Identities via Integration
As the title indicates, this post is going to look at proving some binomial coefficient identities via integration. The first set of identities starts with the expression Now, evaluate this expression in two ways: Do the integration, Swap the sum … Continue reading
Posted in binomial coefficients, calculus
2 Comments