Kassie Archer

collaborators

9 papers

math.CO2026

Pattern avoidance in compositions and powers of permutations

Kassie Archer, Noel Bourne

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

math.CO2026

Permutations that strongly avoid 132

Kassie Archer, Christina Graves

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

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

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 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 $I ¨ $ on ${1, 1, 2, 2, \dots, n, n}$ is called non-crossing if it avoid…