8 citations · 30 across the 12 of their papers we have counts for
16 papers
On balancing two-slice portions of cake
David Bevan
After radial cuts of a circular cake, it is divided into slices. Call an adjacent pair of slices a portion. We exhibit an infinite sequence of cuts such that the ratio betw…
On balancing consecutive slices of cake
David Bevan
Let be an infinite sequence of points on a circle. The first of these points cuts the circle into pieces. For any given , let $μ^r_n(…
Independence of permutation limits at infinitely many scales
David Bevan
We introduce a new natural notion of convergence for permutations at any specified scale, in terms of the density of patterns of restricted width. In this setting we prove that lim…
Permutations with few inversions are locally uniform
David Bevan
We prove that permutations with few inversions exhibit a local-global dichotomy in the following sense. Suppose is a permutation chosen uniformly at random from th…
Bijections between directed animals, multisets and Grand-Dyck paths
Jean-Luc Baril, David Bevan, Sergey Kirgizov
An -multiset of consists of a set of elements from where each element can be repeated. We present the bivariate generating function for -mul…
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…
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…
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…
The permutation class Av(4213,2143)
David Bevan
We determine the structure of permutations avoiding the patterns 4213 and 2143. Each such permutation consists of the skew sum of a sequence of plane trees, together with an increa…
Large butterfly Cayley graphs and digraphs
David Bevan
We present families of large undirected and directed Cayley graphs whose construction is related to butterfly networks. One approach yields, for every large and for values of $…
On the growth of permutation classes
David Bevan
We study aspects of the enumeration of permutation classes, sets of permutations closed downwards under the subpermutation order. First, we consider monotone grid classes of permut…
Intervals of permutation class growth rates
David Bevan
We prove that the set of growth rates of permutation classes includes an infinite sequence of intervals whose infimum is , and that it also contains every value…
The permutation classes Av(1234,2341) and Av(1243,2314)
David Bevan
We investigate the structure of the two permutation classes defined by the sets of forbidden patterns {1234,2341} and {1243,2314}. By considering how the Hasse graphs of permutatio…
Permutations avoiding 1324 and patterns in Łukasiewicz paths
David Bevan
The class Av(1324), of permutations avoiding the pattern 1324, is one of the simplest sets of combinatorial objects to define that has, thus far, failed to reveal its enumerative s…
Growth rates of geometric grid classes of permutations
David Bevan
Geometric grid classes of permutations have proven to be key in investigations of classical permutation pattern classes. By considering the representation of gridded permutations a…
Growth rates of permutation grid classes, tours on graphs, and the spectral radius
David Bevan
Monotone grid classes of permutations have proven very effective in helping to determine structural and enumerative properties of classical permutation pattern classes. Associated…