David I. Bevan

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math.CO2026

On balancing two-slice portions of cake

David Bevan

After $n$ radial cuts of a circular cake, it is divided into $n$ slices. Call an adjacent pair of slices a portion. We exhibit an infinite sequence of cuts such that the ratio betw…

math.CO2026

On balancing consecutive slices of cake

David Bevan

Let $a = (a_{i})_{i = 1}^{\infty}$ be an infinite sequence of points on a circle. The first $n$ of these points cuts the circle into $n$ pieces. For any given $r$ , let $μ^r_n(…

math.CO2019

Bijections between directed animals, multisets and Grand-Dyck paths

Jean-Luc Baril, David Bevan, Sergey Kirgizov

An $n$ -multiset of $[k] = {1, 2, \dots, k}$ consists of a set of $n$ elements from $[k]$ where each element can be repeated. We present the bivariate generating function for $n$ -mul…

math.CO2015

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…