Christina Graves

activity

20232026

collaborators

4 papers

math.CO2026

Permutations that strongly avoid 132

Kassie Archer, Christina Graves

A permutation $π$ strongly avoids the pattern $τ$ if both $π$ and $π^{2}$ avoid $τ$ . In this paper, we enumerate permutations of size $n$ that strongly avoid the pattern 132. This en…

math.CO2025

Binary operations on pattern-avoiding cycles

Kassie Archer, Christina Graves, Robert Laudone

Suppose $c_{n} (σ)$ denotes the number of cyclic permutations in $S_{n}$ that avoid a pattern $σ$ . In this paper, we define partial groupoid structures on cyclic pattern-avoid…

math.CO2024

Pattern-restricted cyclic permutations with a pattern-restricted cycle form

Kassie Archer, Ethan Borsh, Jensen Bridges +2

In this paper, we consider cyclic permutations that avoid the monotone decreasing permutation $k (k - 1) \dots 21$ , whose cycle also demonstrates some pattern avoidance. If the cycle…

math.CO2023

Cyclic permutations avoiding patterns in both one-line and cycle forms

Kassie Archer, Ethan Borsh, Jensen Bridges +2

Let $σ$ and $τ$ be patterns of length three; that is $σ, τ \in {123, 132, 213, 231, 312, 321}$ . In this paper, we enumerate the set of cyclic permutations in $S_{n}$ that avoid…