
Archives
 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: December 2011
The Number of NSEW Lattice Paths with a Maximum Height of y
I’ve been thinking and learning some about lattice path statistics lately, and a couple of days ago I worked out the answer to the following question (with help from some suggestions from Anthony Quas via Math Overflow). Suppose we have … Continue reading
Posted in combinatorics, lattice paths
Leave a comment
Checking Multiplication via Digit Sums
Last week a friend who is a fourth grade teacher came to me with a math problem. The father of one of his students had showed him a trick for checking the result of a threedigit multiplication problem. The father … Continue reading
Posted in arithmetic, elementary number theory
4 Comments
A Combinatorial Proof of a Formula Involving Euler’s Totient Function
Several years ago I found a proof of the following identity, which I had not seen before (and still haven’t seen anywhere else): where is Euler’s totient function, the number of positive integers less than or equal to and relatively … Continue reading
Posted in combinatorics, elementary number theory
2 Comments
The Duality “Gap” in Linear Programming
Wait… what? Doesn’t the strong duality theorem imply that there is no duality gap in linear programming? Mostly, yes, although there is a sense in which there actually is a duality gap; it occurs when the primal and dual problems … Continue reading
Posted in linear programming, optimization
3 Comments
Solving TwoTerm Combinatorial Recurrence Relations
Many named combinatorial numbers satisfy the following general twoterm combinatorial recurrence relation: For example: Binomial coefficients: Stirling cycle numbers: Stirling subset numbers: Lah numbers: Eulerian numbers: Secondorder Eulerian numbers: It is not known how to solve the recurrence in general. … Continue reading
Posted in combinatorics, recurrence relations
1 Comment
Harmonic Numbers and Stirling Numbers
This post will present three proofs of the following representation of harmonic numbers in terms of Stirling cycle numbers (or unsigned Stirling numbers of the first kind): Each proof uses a different property of the Stirling numbers. Proof 1: … Continue reading
Posted in combinatorics, sequences and series
Leave a comment
Generating Geometric and Truncated Exponential Random Variates
If you do numerical simulations you often find yourself needing to generate random variates from a specific distribution. There are several techniques for doing this, such as the inverse transform method and the acceptanceandrejection method. This post will talk about … Continue reading
Posted in probability, simulation
Leave a comment