Kassie Archer

collaborators

4 papers

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.CO2024

Pattern avoidance and the fundamental bijection

Kassie Archer, Robert P. Laudone

The fundamental bijection is a bijection $θ : S_{n} \to S_{n}$ in which one uses the standard cycle form of one permutation to obtain another permutation in one-line fo…

math.CO2024

Descents in powers of permutations

Kassie Archer, Aaron Geary

We consider a few special cases of the more general question: How many permutations $π \in S_{n}$ have the property that $π^{2}$ has $j$ descents for some $j$ ? In this paper, w…

math.CO2024

Pattern-restricted permutations of small order

Kassie Archer, Robert P. Laudone

We enumerate 132-avoiding permutations of order 3 in terms of the Catalan and Motzkin generating functions, answering a question of Bóna and Smith from 2019. We also enumerate 231-…