Kassie Archer

activity

20132026

most citedPattern restricted quasi-Stirling permutations

14 citations · 26 across the 27 of their papers we have counts for

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30 papers · 1 filter

math.CO2026

Pattern restricted parking functions with limited preferences

Kassie Archer, Robert Laudone

A parking function is said to have $ℓ$ -limited preferences if there are at most $ℓ$ copies of each element in the parking function. In this paper, we define a notion of patte…

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.CO2026

Arrow pattern avoidance in permutations: structure and enumeration

Kassie Archer, Robert P. Laudone

Arrow patterns were introduced by Berman and Tenner as a generalization of vincular patterns. They observed that arrow patterns have the potential to bridge the divide between a pe…

math.CO2025

Seaweed algebras with restricted part sizes

Kassie Archer, Aaron Geary, Robert P. Laudone

Seaweed algebras are a class of Lie algebras that are naturally characterized by a pair of compositions, which in turn are represented visually as planar graphs called meanders. Th…

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.CO2025

Generalized chip firing and critical groups of arithmetical structures on trees

Kassie Archer, Alexander Diaz-Lopez, Darren Glass +1

Chip firing provides a way to study the sandpile group (also known as the Jacobian) of a graph. We use a generalized version of chip firing to bound the number of invariant factors…

math.CO2025

Pattern avoidance in compositions and powers of permutations

Kassie Archer, Noel Bourne

A permutation $π$ is said to avoid a chain $(σ : τ)$ of patterns if $π$ avoids $σ$ and $π^{2}$ avoids $τ .$ In this paper, we define a notion of pattern avoidance for compositions of po…

math.CO2025

Harmonic Morphisms of Arithmetical Structures on Graphs

Kassie Archer, Caroline Melles

Let $ϕ : Γ_{2} \to Γ_{1}$ be a harmonic morphism of connected graphs. We show that an arithmetical structure on $Γ_{1}$ can be pulled back via $ϕ$ to an arithmetical structur…

math.CO2025

Pattern avoidance in non-crossing and non-nesting permutations

Kassie Archer, Robert P. Laudone

Non-crossing and non-nesting permutations are variations of the well-known Stirling permutations. A permutation $π$ on ${1, 1, 2, 2, \dots, n, n}$ is called non-crossing if it avoids…

math.CO2025

Pattern-avoiding shallow permutations

Kassie Archer, Aaron Geary, Robert P. Laudone

Shallow permutations were defined in 1977 to be those that satisfy the lower bound of the Diaconis-Graham inequality. Recently, there has been renewed interest in these permutation…

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-…

math.CO2023

Powers of permutations that avoid chains of patterns

Kassie Archer, Aaron Geary

In a recent paper, Bona and Smith define the notion of \textit{strong avoidance}, in which a permutation and its square both avoid a given pattern. In this paper, we generalize thi…

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…

math.CO2023★ 1 cited

Critical groups of arithmetical structures on star graphs and complete graphs

Kassie Archer, Alexander Diaz-Lopez, Darren Glass +1

An arithmetical structure on a finite, connected graph without loops is an assignment of positive integers to the vertices that satisfies certain conditions. Associated to each of…

math.CO2022

A new statistic on Dyck paths for counting 3-dimensional Catalan words

Kassie Archer, Christina Gravies

A 3-dimensional Catalan word is a word on three letters so that the subword on any two letters is a Dyck path. For a given Dyck path $D$ , a recently defined statistic counts the nu…

math.CO2021

Pattern-restricted permutations composed of 3-cycles

Kassie Archer, Christina Graves

In this paper, we characterize and enumerate pattern-avoiding permutations composed of only 3-cycles. In particular, we answer the question for the six patterns of length 3. We fin…

math.CO2019★ 1 cited

Counting acyclic and strong digraphs by descents

Kassie Archer, Ira M. Gessel, Christina Graves +1

A descent of a labeled digraph is a directed edge (s, t) with s > t. We count strong tournaments, strong digraphs, and acyclic digraphs by descents and edges. To count strong tourn…

math.CO2019★ 8 cited

Arithmetical structures on bidents

Kassie Archer, Abigail Bishop, Alexander Diaz-Lopez +3

An arithmetical structure on a finite, connected graph $G$ is a pair of vectors $(d, r)$ with positive integer entries for which $(\operatorname{diag}(\mathbf{d})…

math.CO2018★ 14 cited

Pattern restricted quasi-Stirling permutations

Kassie Archer, Adam Gregory, Bryan Pennington +1

We define a variation of Stirling permutations, called quasi-Stirling permutations, to be permutations on the multiset ${1, 1, 2, 2, \dots, n, n}$ that avoid the patterns 1212 and 21…

math.CO2018

Involutions and the Gelfand character

Kassie Archer, Virginia Germany, C. Marin King +1

The Gelfand representation of $S_{n}$ is the multiplicity-free direct sum of the irreducible representations of $S_{n}$ . In this paper, we use a result of Adin, Pos…

math.CO2018

Enumerating two permutation classes by the number of cycles

Kassie Archer

We enumerate permutations in the two permutation classes $Av_{n} (312, 4321)$ and $Av_{n} (321, 4123)$ by the number of cycles each permutation admits. We also refine this…