All Questions

It very often happens that one reduces a problem to a bunch of combinatorial data, and need to sift through this data for patterns, which form conjectures on which to do "real" mathematics. ...

Let $\mathbb{N}$ denote the set of positive integers, and let $G=(V,E)$ be a finite simple, undirected graph. Given $f:V\to \mathbb{Z}$ we define the neighborhood sum function $\mathrm{nsum}_f:V\to\...

Let $\text{Mat}(n\times n,\mathbb{Z})$ denote the collection of integer $n\times n$ matrices. We say $M\in \text{Mat}(n\times n,\mathbb{Z})$ is a power matrix if there is an integer $k>1$ and a ...

Given a formal grammar of a language or an Turing machine of the language, can we count the path that generating sentences of the language? For example, we know that if the grammar is context-free ...