E. Schmutz

activity

20022025

most citedIterating random functions on a finite set

9 citations · 23 across the 9 of their papers we have counts for

collaborators

11 papers

math.CO2025

Cardinalities of $g$ -difference sets

Eric Schmutz, Michael Tait

Let $η_{g} (n)$ be the smallest cardinality that $A \subseteq Z$ can have if $A$ is a $g$ -difference basis for $[n]$ (i.e, if, for each $x \in [n]$ , there are {\em at least…

math.CO2018

Permutations With Equal Orders

Huseyin Acan, Charles Burnette, Sean Eberhard +2

Let $P (n)$ be the probability that two independent, uniformly random permutations of $[n]$ have the same order, and let $K (n)$ be the probability that they are in the same conjugac…

math.CO2017

Periods of iterations of functions with restricted preimage sizes

Rodrigo S. V. Martins, Daniel Panario, Claudio Qureshi +1

We consider random mappings on n = kr nodes with preimage sizes restricted to a set of the form {0,k}, where k = k(r) is greater than 1. We prove that T, the least common multiple…

math.NT2015★ 8 cited

Periods of Iterated Rational Functions over a Finite Field

Charles Burnette, Eric Schmutz

Choose a random degree d poly f with coefficients in a finite field F. We estimate the ultimate period of f under compositional iteration. We also determine the joint distribution…

math.CO2015★ 3 cited

Representing Random Permutations as the Product of Two Involutions

Charles Burnette, Eric Schmutz

An involution is a permutation that is its own inverse. Given a permutation $σ$ of $[n],$ let $N_{n} (σ)$ denote the number of ways to write $σ$ as a product of two involut…

math.CO2012

Part-products of $S$ -restricted integer compositions

Eric Schmutz, Caroline Shapcott

If $S$ is a cofinite set of positive integers, an " $S$ -restricted composition of $n$ " is a sequence of elements of $S$ , denoted $λ = (λ_{1}, λ_{2}, ...)$ , whose sum is $n$ . For uniform…