6 citations · 12 across the 18 of their papers we have counts for
12 papers · 1 filter
Pattern restricted parking functions with limited preferences
Kassie Archer, Robert Laudone
A parking function is said to have -limited preferences if there are at most copies of each element in the parking function. In this paper, we define a notion of patte…
Pattern avoidance in canon permutations
Robert Laudone
A canon permutation is a -regular word over in which, for each , the -th copies of the letters form the same permutation . These were introduced by Elizalde as a…
A lower bound on the growth rate of -avoiding cyclic permutations
Robert Laudone
We construct a new reduction process which takes a -avoiding permutation to a shorter one that is cyclic if and only if the original was. Iterating it determines whether…
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…
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…
Characterizing avoidance in cycles via vincular patterns
Robert P. Laudone
We show that cyclic permutations avoiding are precisely those permutations whose image under the fundamental bijection avoid a set of vincular patterns. We do this by using p…
Binary operations on pattern-avoiding cycles
Kassie Archer, Christina Graves, Robert Laudone
Suppose denotes the number of cyclic permutations in that avoid a pattern . In this paper, we define partial groupoid structures on cyclic pattern-avoid…
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 on is called non-crossing if it avoids…
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…
Pattern avoidance and the fundamental bijection
Kassie Archer, Robert P. Laudone
The fundamental bijection is a bijection in which one uses the standard cycle form of one permutation to obtain another permutation in one-line fo…
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-…
A counterexample to a Gröbner approach for noetherianity of the twisted commutative algebra
Robert P. Laudone
We resolve an open question posed by the authors of arXiv:1501.06925v2 in 2015 concerning a Gröbner theoretic approach for the noetherianity of the twisted commutative algebra ${\r…