10 citations · 16 across the 11 of their papers we have counts for
12 papers
Enumeration of pattern-avoiding alternating sign matrices: An asymptotic dichotomy
Mathilde Bouvel, Eric S. Egge, Rebecca N. Smith +2
We completely classify the asymptotic behavior of the number of alternating sign matrices classically avoiding a single permutation pattern, in the sense of [Johansson and Linusson…
Growth Rates Of Permutations With Given Descent Or Peak Set
Mohamed Omar, Justin M. Troyka
Given a set , consider the sequences where for any , and respectively count the number of permutations in the s…
Statistics on clusters and -Stirling permutations
Sergi Elizalde, Justin M. Troyka, Yan Zhuang
The Goulden$\unicode{x2013}$Jackson cluster method, adapted to permutations by Elizalde and Noy, reduces the problem of counting permutations by occurrences of a prescribed consecu…
Fibonacci numbers, consecutive patterns, and inverse peaks
Justin M. Troyka, Yan Zhuang
We give multiple proofs of two formulas concerning the enumeration of permutations avoiding a monotone consecutive pattern with a certain value for the inverse peak number or inver…
On pattern avoidance in matchings and involutions
Jonathan J. Fang, Zachary Hamaker, Justin M. Troyka
We study the relationship between two notions of pattern avoidance for involutions in the symmetric group and their restriction to fixed-point-free involutions. The first is classi…
Bounded affine permutations II. Avoidance of decreasing patterns
Neal Madras, Justin M. Troyka
We continue our study of a new boundedness condition for affine permutations, motivated by the fruitful concept of periodic boundary conditions in statistical physics. We focus on…
Bounded affine permutations I. Pattern avoidance and enumeration
Neal Madras, Justin M. Troyka
We introduce a new boundedness condition for affine permutations, motivated by the fruitful concept of periodic boundary conditions in statistical physics. We study pattern avoidan…
Period mimicry: A note on the -evaluation of the peak polynomials
Justin M. Troyka
We briefly explore a sequence that came up in recent work of Tirrell and Zhuang. We discover an unusual phenomenon where the sequence appears at first to have periodic behavior but…
On the centrosymmetric permutations in a class
Justin M. Troyka
A permutation is centrosymmetric if it is fixed by a half-turn rotation of its diagram. Initially motivated by a question by Alexander Woo, we investigate the question of whether t…
Split graphs: combinatorial species and asymptotics
Justin M. Troyka
A split graph is a graph whose vertices can be partitioned into a clique and a stable set. We investigate the combinatorial species of split graphs, providing species-theoretic gen…
Exact and asymptotic enumeration of cyclic permutations according to descent set
Sergi Elizalde, Justin M. Troyka
Using a result of Gessel and Reutenauer, we find a simple formula for the number of cyclic permutations with a given descent set, by expressing it in terms of ordinary descent numb…
Combinatorial species and graph enumeration
Andy Hardt, Pete McNeely, Tung Phan +1
In enumerative combinatorics, it is often a goal to enumerate both labeled and unlabeled structures of a given type. The theory of combinatorial species is a novel toolset which pr…