Eric Rowland Hi! I'm a professor in the Department of Mathematics at Hofstra University. On my YouTube channel, I make videos about discoveries in number theory. You can also watch some of my research talks.
I'm currently writing a book, My research is broadly in number theory and combinatorics. I make extensive use of software for conducting experiments, discovering conjectures, and proving theorems. As a graduate student, I proved that a recurrence discovered in 2003 generates primes. (I made a video about it.)
One of my main interests is in studying arithmetic properties of integer sequences that arise in combinatorics.
Binomial coefficients are a classic example of an enumeration question producing numbers with interesting properties.
I discovered a matrix product for counting binomial coefficients according to the highest power of There are many sequences in combinatorics (for example, the famous Catalan numbers) that, when reduced modulo prime powers, are generated by automata. Here is a quick introduction. Reem Yassawi and I used this to produce wholesale congruence theorems for algebraic sequences and, more generally, diagonals of rational functions. This subsumes many results in the literature on specific sequences, and it allowed us to answer several open questions. Doron Zeilberger and I showed that a similar technique works for constant-term sequences. Moreover, we have bounds on the size of the automaton modulo primes and modulo prime powers (forthcoming); this determines the time complexity for computing the automaton.
In combinatorics on words, I have written papers with Jeff Shallit, Lara Pudwell, Manon Stipulanti, and a team of undergraduates in the Polymath Jr program on extremal integer sequences avoiding repetitions of various kinds. These sequences are self-similar, but the structures are on such large scales that they can only be found with a computer. I'm a big proponent of communicating mathematics as clearly and accessibly as possible. I've collected some advice on writing and refereeing. ... among other things. Here are more systematic lists: - papers (also on the arXiv)
- talks
*Mathematica*packages- computed data
Here is my CV, but what's not on my CV is that my favorite LaTeX command is I highly recommend A Mathematician's Lament by Paul Lockhart (2002) [also available in paperback] and the introduction by Keith Devlin. |