13 citations · 21 across the 6 of their papers we have counts for
11 papers · 1 filter
The Four Point Permutation Test for Latent Block Structure in Incidence Matrices
R W R Darling, Cheyne Homberger
Transactional data may be represented as a bipartite graph , where denotes agents, denotes objects visible to many agents, and an edge in denotes an i…
The minimum Manhattan distance and minimum jump of permutations
Simon R. Blackburn, Cheyne Homberger, Peter Winkler
Let be a permutation of . If we identify a permutation with its graph, namely the set of dots at positions , it is natural to consider the minim…
Prolific permutations and permuted packings: downsets containing many large patterns
David Bevan, Cheyne Homberger, Bridget Eileen Tenner
A permutation of n letters is k-prolific if each (n-k)-subset of the letters in its one-line notation forms a unique pattern. We present a complete characterization of k-prolific p…
Generating Permutations with Restricted Containers
Michael H. Albert, Cheyne Homberger, Jay Pantone +2
We investigate a generalization of stacks that we call -machines. We show how this viewpoint rapidly leads to functional equations for the classes of permutations that…
Equipopularity Classes in the Separable Permutations
Michael Albert, Cheyne Homberger, Jay Pantone
When two patterns occur equally often in a set of permutations, we say that these patterns are equipopular. Using both structural and analytic tools, we classify the equipopular pa…
Patterns in Permutations and Involutions: A Structural and Enumerative Approach
Cheyne Homberger
This dissertation presents a multifaceted look into the structural decomposition of permutation classes. The theory of permutation patterns is a rich and varied field, and is a pri…
Deflatability of Permutation Classes
M. H. Albert, M. D. Atkinson, Cheyne Homberger +1
A deflatable permutation class is one in which the simple permutations are contained in a proper subclass. Deflatable permutation classes are often easier to describe and enumerate…
Pattern-Avoiding Involutions: Exact and Asymptotic Enumeration
Miklós Bóna, Cheyne Homberger, Jay Pantone +1
We consider the enumeration of pattern-avoiding involutions, focusing in particular on sets defined by avoiding a single pattern of length 4. As we demonstrate, the numerical data…
On the effective and automatic enumeration of polynomial permutation classes
Cheyne Homberger, Vince Vatter
We describe an algorithm, implemented in Python, which can enumerate any permutation class with polynomial enumeration from a structural description of the class. In particular, th…
Counting Fixed-Length Permutation Patterns
Cheyne Homberger
We consider the problem of packing fixed-length patterns into a permutation, and develop a connection between the number of large patterns and the number of bonds in a permutation.…
Expected Patterns in Permutation Classes
Cheyne Homberger
In the set of all patterns in , it is clear that each k-pattern occurs equally often. If we instead restrict to the class of permutations avoiding a specific pattern, the situ…