Robert C. Rhoades
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View article: Numerical simulation of the trapping reaction with mobile and reacting traps
Numerical simulation of the trapping reaction with mobile and reacting traps Open
We study a variation of the trapping reaction, A+B→A, in which both the traps (A) and the particles (B) undergo diffusion, and the traps upon meeting react according to A+A→0 or A. This two-species reaction-diffusion system is known to exh…
View article: Peak positions of strongly unimodal sequences
Peak positions of strongly unimodal sequences Open
We study combinatorial and asymptotic properties of the rank of strongly unimodal sequences. We find a generating function for the rank enumeration function and give a new combinatorial interpretation of the ospt-function introduced by And…
View article: A PROOF OF ANDREWS’ CONJECTURE ON PARTITIONS WITH NO SHORT SEQUENCES
A PROOF OF ANDREWS’ CONJECTURE ON PARTITIONS WITH NO SHORT SEQUENCES Open
Our main result establishes Andrews’ conjecture for the asymptotic of the generating function for the number of integer partitions of $n$ without $k$ consecutive parts. The methods we develop are applicable in obtaining asymptotics for sto…
View article: Counting De Bruijn sequences as perturbations of linear recursions
Counting De Bruijn sequences as perturbations of linear recursions Open
Every binary De~Bruijn sequence of order n satisfies a recursion 0=x_n+x_0+g(x_{n-1}, ..., x_1). Given a function f on (n-1) bits, let N(f; r) be the number of functions generating a De Bruijn sequence of order n which are obtained by chan…
View article: Integer partitions, probabilities and quantum modular forms
Integer partitions, probabilities and quantum modular forms Open
What is the probability that the smallest part of a random integer partition of N is odd? What is the expected value of the smallest part of a random integer partition of N? It is straightforward to see that the answers to these questions …