Colin Defant

activity

20142026

most citedStack-Sorting Preimages of Permutation Classes

12 citations · 98 across the 59 of their papers we have counts for

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Showing 2015Show all

14 papers · 1 filter

math.CO2015

Flexible Toggles and Symmetric Invertible Asynchronous Elementary Cellular Automata

Colin Defant

A sequential dynamical system (SDS) consists of a graph $G$ with vertices $v_{1}, v_{2}, \dots, v_{n}$ , a state set $A$ , a collection of "vertex functions" ${f_{v_{i}}}_{i = 1}^{n}$ , and a per…

math.CO2015

Preimages under the Stack-Sorting Algorithm

Colin Defant

We use a method for determining the number of preimages of any permutation under the stack-sorting map in order to obtain recursive upper bounds for the numbers $W_{t} (n)$ and $W_t(n…

math.CO2015★ 1 cited

Binary Codes and Period-2 Orbits of Sequential Dynamical Systems

Colin Defant

Let $[K_{n}, f, π]$ be the (global) SDS map of a sequential dynamical system (SDS) defined over the complete graph $K_{n}$ using the update order $π \in S_{n}$ in which all vertex functions…

math.NT2015

On Ranges of Variants of the Divisor Functions that are Dense

Colin Defant

For a real number $t$ , let $s_{t}$ be the multiplicative arithmetic function defined by $s_{t} (p^{α}) = j = 0 \sum α (- p^{t})^{j}$ for all primes $p$ and positive integers $α$ . W…

math.NT2015★ 2 cited

On the Density of Ranges of Generalized Divisor Functions with Restricted Domains

Colin Defant

We begin by defining functions $σ_{t, k}$ , which are generalized divisor functions with restricted domains. For each positive integer $k$ , we show that, for $r > 1$ , the range of $σ_{…

math.NT2015

Ranges of Unitary Divisor Functions

Colin Defant

For any real $t$ , the unitary divisor function $σ_{t}^{*}$ is the multiplicative arithmetic function defined by $σ_{t}^{*} (p^{α}) = 1 + p^{α t}$ for all primes $p$ and positive integers $α$ . Let…