Category Archives: Combinatorics

The discrete Gauss-Bonnet theorem

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

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 | 2 Comments

A Fibonacci-like sequence

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+…

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