10 citations · 42 across the 17 of their papers we have counts for
18 papers · 1 filter
Stretched exponential asymptotics for bases of triangular bootstrap percolation
Andrew Elvey Price, Juliette Schabanel, Paul Thévenin
In this paper, we study a bootstrap percolation process on the finite triangular grid of side length . We say that a subset of points in pe…
Enumeration of three quadrant walks with small steps and walks on other M-quadrant cones
Andrew Elvey Price
We address the enumeration of walks with small steps confined to a two-dimensional cone, for example the quarter plane, three-quarter plane or the slit plane. In the quarter plane…
Pattern-avoiding ascent sequences of length 3
Andrew R Conway, Miles Conway, Andrew Elvey Price +1
Pattern-avoiding ascent sequences have recently been related to set-partition problems and stack-sorting problems. While the generating functions for several length-3 pattern-avoid…
Asymptotics of 3-stack-sortable permutations
Colin Defant, Andrew Elvey Price, Anthony J Guttmann
We derive a simple functional equation with two catalytic variables characterising the generating function of 3-stack-sortable permutations. Using this functional equation, we exte…
Bijections between walks inside a triangular domain and Motzkin paths of bounded amplitude
Julien Courtiel, Andrew Elvey Price, Irène Marcovici
This paper solves an open question of Mortimer and Prellberg asking for an explicit bijection between two families of walks. The first family is formed by what we name triangular w…
The six-vertex model on random planar maps revisited
Andrew Elvey Price, Paul Zinn-Justin
We address the six vertex model on a random lattice, which in combinatorial terms corresponds to the enumeration of weighted 4-valent planar maps equipped with an Eulerian orientat…
Counting lattice walks by winding angle
Andrew Elvey Price
We address the problem of counting walks by winding angle on the Kreweras lattice, an oriented version of the triangular lattice. Our method uses a new decomposition of the lattice…
Phylogenetic trees, augmented perfect matchings, and a Thron-type continued fraction (T-fraction) for the Ward polynomials
Andrew Elvey Price, Alan D. Sokal
We find a Thron-type continued fraction (T-fraction) for the ordinary generating function of the Ward polynomials, as well as for some generalizations employing a large (indeed inf…
Stieltjes moment sequences for pattern-avoiding permutations
Alin Bostan, Andrew Elvey Price, Anthony John Guttmann +1
A small set of combinatorial sequences have coefficients that can be represented as moments of a nonnegative measure on . Such sequences are known as Stieltjes moment…
Permutations sortable by deques and two stacks in parallel share the same growth rate
Andrew Elvey Price
Recently Albert and Bousquet-Mélou obtained the solution to the long-standing problem of the enumeration of permutations sortable by two stacks in parallel (2sip). Their solution w…
Compacted binary trees admit a stretched exponential
Andrew Elvey Price, Wenjie Fang, Michael Wallner
A compacted binary tree is a directed acyclic graph encoding a binary tree in which common subtrees are factored and shared, such that they are represented only once. We show that…
Eulerian orientations and the six-vertex model on planar map
Mireille Bousquet-Mélou, Andrew Elvey Price, Paul Zinn-Justin
We address the enumeration of planar 4-valent maps equipped with an Eulerian orientation by two different methods, and compare the solutions we thus obtain. With the first method w…
The generating function of planar Eulerian orientations
Mireille Bousquet-Mélou, Andrew Elvey Price
The enumeration of planar maps equipped with an Eulerian orientation has attracted attention in both combinatorics and theoretical physics since at least 2000. The case of 4-valent…
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…
Counting Planar Eulerian Orientations
Andrew Elvey Price, Anthony J Guttmann
Inspired by the paper of Bonichon, Bousquet-Mélou, Dorbec and Pennarun, we give a system of functional equations which characterise the ordinary generating function, for th…
The isoperimetric number of the incidence graph of PG(n,q)
Andrew Elvey Price, Muhammad Adib Surani, Sanming Zhou
Let be the point-hyperplane incidence graph of the projective space , where is an integer and a prime power. We determine the order…
Permutations sortable by two stacks in series
Andrew Elvey Price, Anthony J Guttmann
We address the problem of the number of permutations that can be sorted by two stacks in series. We do this by first counting all such permutations of length less than 20 exactly,…
Permutations sortable by deques and by two stacks in parallel
Andrew Elvey Price, Anthony J. Guttmann
Recently Albert and Bousquet-Mélou \cite{AB15} obtained the solution to the long-standing problem of the number of permutations sortable by two stacks in parallel (tsip). Their sol…