Category Archives: Combinatorics

Noncommutative probability II: independence

Posted on 27/07/2018 by lamwk

Recall that two random variables and are said to be independent if for all Borel sets . We don’t have a probability measure behind the abstract definition of noncommutative probability space, so we cannot define independence in this way. However, … Continue reading →

Posted in Combinatorics, Probability | Leave a comment

The discrete Gauss-Bonnet theorem

Posted on 21/06/2016 by KKK

This is a slight extension of my previous note on discrete Gauss-Bonnet theorem. As mentioned in that note, this is a generalization of the well-known fact that the sum of the exterior angles of a polygon is always , which … Continue reading →

Posted in Calculus, Combinatorics, Discrete Mathematics, Geometry, Topology | Leave a comment

Toric perspective 1

Posted on 23/05/2015 by HL

This series of posts will be about toric varieties. The author is not sure if there is a part 2, but he still calls this part 1. This post is about computing the dimensions and degrees of popular toric varieties. … Continue reading →

Posted in Algebraic geometry, Combinatorics | 4 Comments

A Fibonacci-like sequence

Posted on 05/03/2015 by KKK

What’s the pattern of the following sequence? Can you guess the next term? The answer is

Posted in Algebra, Combinatorics | Leave a comment

Some thoughts on 1+2+3+…

Posted on 04/05/2013 by KKK

This post is a rather dumb one – and, contrary to the title, the emphasis is not on . In fact, I just put some of my dumb thoughts here after reading a comment of Terry Tao in his own … Continue reading →

Posted in Combinatorics | Leave a comment