We shall show an upper bound on the Stirling number of the second kind, a byproduct of a homework exercise of Probabilistic Combinatorics offered by Prof. Tom Bohman. Definition. A Stirling number of the second kind (or Stirling partition number) is the number of ways to partition a set of objects into non-empty subsets and… Continue reading An Upper Bound on Stirling Number of the Second Kind
Tag: probabilistic method
A Probabilistic Proof of Isoperimetric Inequality
This note is based on Nicolas Garcia Trillos’ talk, Some Problems and Techniques in Geometric Probability, at Carnegie Mellon University on January 29, 2015. In particular, we demonstrate a probabilistic proof of the isoperimetric inequality. The proof can also be found in Integral Geometry and Geometric Probability by Luis A. Santaló. Theorem. For a convex set… Continue reading A Probabilistic Proof of Isoperimetric Inequality