Name: Marla Slusky
Email: mslusky at eden dot rutgers dot edu
Medina and Doron
p-adic valuation of
Introduction to my project:
Sometimes, if you take the
p-adic valutation of every
number in a sequence, you get really pretty patterns. For example,
if we graph the 3-adic valuation of the integers, we get this pretty
We can also look at a sequence of binomial coefficients.
This picture shows the 3-adic
valuation of the integers choose 7
Which has similar characteristics.
Stirling numbers of the second kind have some similar
characteristics, but are a little less predictable.
However, last summer, 3 REU students, Ana Berrizbeitia, Alexander Moll, and
Laine Noble, researched p-adic valuation of Stirling numbers of the
second kind, and were able to formalize the behavior.
My goal is to do something similar for the even less well behaved
These three types of sequences, Binomial Coefficients, Stirling
numbers of the second kind, and Eulerian numbers are all examples of
triangular recurrences. My REU project is just one case of a more
general problem: Can the p-adic valuation of all triagular recurrences
be neatly described? and if the answer is no, then what is it about
these sequences that makes them well behaved?
I did an REU in 2006 about Matrix Polynomials with
Robert Wilson. That
project is here
Also, check out my skyscraper puzzles (Skyscraper Puzzles)