13 citations · 34 across the 13 of their papers we have counts for
23 papers
Permutation classes need not have proper growth rates
Jay Pantone, Vincent Vatter
By the Marcus-Tardos Theorem (formerly the Stanley-Wilf Conjecture), every permutation class other than the class of all permutations has a finite upper growth rate, meaning that t…
Exactly-solvable self-trapping lattice walks. II. Lattices of arbitrary height
Jay Pantone, Alexander R. Klotz, Everett Sullivan
A growing self-avoiding walk (GSAW) is a walk on a graph that is directed, does not visit the same vertex twice, and has a trapped endpoint. We show that the generating function en…
Combinatorial Exploration: An algorithmic framework for enumeration
Michael H. Albert, Christian Bean, Anders Claesson +3
Combinatorial Exploration is a new domain-agnostic algorithmic framework to automatically and rigorously study the structure of combinatorial objects and derive their counting sequ…
Permutations avoiding sets of patterns with long monotone subsequences
Miklós Bóna, Jay Pantone
We enumerate permutations that avoid all but one of the patterns of length starting with a monotone increasing subsequence of length . We compare the size of such perm…
Colored Multipermutations and a Combinatorial Generalization of Worpitzky's Identity
John Engbers, Jay Pantone, Christopher Stocker
Worpitzky's identity expresses in terms of the Eulerian numbers and binomial coefficients: Pita-Ruiz recent…
Counting pop-stacked permutations in polynomial time
Anders Claesson, Bjarki Ágúst Guðmundsson, Jay Pantone
Permutations in the image of the pop-stack operator are said to be pop-stacked. We give a polynomial-time algorithm to count pop-stacked permutations up to a fixed length and we us…
Completing the Structural Analysis of the 2x4 Permutation Classes
Samuel Miner, Jay Pantone
We study the structure and enumeration of the final two 2x4 permutation classes, completing a research program that has spanned almost two decades. For both classes, careful struct…
A structural characterisation of Av(1324) and new bounds on its growth rate
David Bevan, Robert Brignall, Andrew Elvey Price +1
We establish an improved lower bound of 10.271 for the exponential growth rate of the class of permutations avoiding the pattern 1324, and an improved upper bound of 13.5. These re…
Universal layered permutations
Michael Albert, Michael Engen, Jay Pantone +1
We establish an exact formula for the length of the shortest permutation containing all layered permutations of length , proving a conjecture of Gray.
Shift equivalence in the generalized factor order
Jennifer Fidler, Daniel Glasscock, Brian Miceli +2
We provide a geometric condition that guarantees strong Wilf equivalence in the generalized factor order. This provides a powerful tool for proving specific and general Wilf equiva…
On the growth of merges and staircases of permutation classes
Michael Albert, Jay Pantone, Vincent Vatter
There is a well-known upper bound on the growth rate of the merge of two permutation classes. Curiously, there is no known merge for which this bound is not achieved. Using stairca…
Is the full susceptibility of the square-lattice Ising model a differentially algebraic function?
A. J. Guttmann, I. Jensen, J-M. Maillard +1
We study the class of non-holonomic power series with integer coefficients that reduce, modulo primes, or powers of primes, to algebraic functions. In particular we try to determin…
The Asymptotic Number of Simple Singular Vector Tuples of a Cubical Tensor
Jay Pantone
S. Ekhad and D. Zeilberger recently proved that the multivariate generating function for the number of simple singular vector tuples of a generic ten…
Growth rates of permutation classes: categorization up to the uncountability threshold
Jay Pantone, Vincent Vatter
In the antecedent paper to this it was established that there is an algebraic number such that while there are uncountably many growth rates of permutation class…
Pattern avoidance in forests of binary shrubs
David Bevan, Derek Levin, Peter Nugent +4
We investigate pattern avoidance in permutations satisfying some additional restrictions. These are naturally considered in terms of avoiding patterns in linear extensions of certa…
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…
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…
On the Rearrangement Conjecture for Generalized Factor Order Over
Jay Pantone, Vincent Vatter
The Rearrangement Conjecture states that if two words over are Wilf-equivalent in the factor order on then they are rearrangements of each other. We…
On Isomorphism Classes of Generalized Fibonacci Cubes
Jernej Azarija, Sandi Klavžar, Jaehun Lee +2
The generalized Fibonacci cube is the subgraph of the -cube induced on the set of all strings of length that do not contain as a substring. It is proved t…
Two Examples of Unbalanced Wilf-Equivalence
Alexander Burstein, Jay Pantone
We prove that the set of patterns {1324,3416725} is Wilf-equivalent to the pattern 1234 and that the set of patterns {2143,3142,246135} is Wilf-equivalent to the set of patterns {2…
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…
The Enumeration of Permutations Avoiding 3124 and 4312
Jay Pantone
We find the generating function for the class of all permutations that avoid the patterns 3124 and 4312 by showing that it is an inflation of the union of two geometric grid classe…