4 papers · 1 filter
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…
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…
Descents in powers of permutations
Kassie Archer, Aaron Geary
We consider a few special cases of the more general question: How many permutations have the property that has descents for some ? In this paper, w…
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…