University of Otago

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19932026

most citedThe role of artificial intelligence in achieving the Sustainable Development Goals

3.2k citations

researchers with a paper here

Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

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28 papers · 1 filter

math.CO2022★ 2 cited

A logical limit law for $231$ -avoiding permutations

Michael Albert, Mathilde Bouvel, Valentin Féray +1

We prove that the class of 231-avoiding permutations satisfies a logical limit law, i.e. that for any first-order sentence $Ψ$ , in the language of two total orders, the probability…

math.CO2019

Two examples of Wilf-collapse

Michael Albert, Vít Jelínek, Michal Opler

Two permutation classes, the X-class and subpermutations of the increasing oscillation are shown to exhibit an exponential Wilf-collapse. This means that the number of distinct enu…

math.CO2019★ 5 cited

Asymmetric function theory

Oliver Pechenik, Dominic Searles

The classical theory of symmetric functions has a central position in algebraic combinatorics, bridging aspects of representation theory, combinatorics, and enumerative geometry. M…

math.CO2019

Uniquely-Wilf classes

Michael Albert, Jinge Li

Two permutations in a class are Wilf-equivalent if, for every size, $n$ , the number of permutations in the class of size $n$ containing each of them is the same. Those infinite cla…

math.CO2018★ 7 cited

Polynomials from combinatorial $K$ -theory

Cara Monical, Oliver Pechenik, Dominic Searles

We introduce two new bases of the ring of polynomials and study their relations to known bases. The first basis is the quasiLascoux basis, which is simultaneously both a $K$ -theore…

math.CO2017

Characterising inflations of monotone grid classes of permutations

Michael Albert, Aistis Atminas, Robert Brignall

We characterise those permutation classes whose simple permutations are monotone griddable. This characterisation is obtained by identifying a set of nine substructures, at least o…

math.CO2015

$2 \times 2$ monotone grid classes are finitely based

Michael Albert, Robert Brignall

In this note, we prove that all $2 \times 2$ monotone grid classes are finitely based, i.e., defined by a finite collection of minimal forbidden permutations. This follows from a s…

math.CO2015★ 6 cited

The Complexity of Pattern Matching for $321$ -Avoiding and Skew-Merged Permutations

Michael H. Albert, Marie-Louise Lackner, Martin Lackner +1

The Permutation Pattern Matching problem, asking whether a pattern permutation $π$ is contained in a permutation $τ$ , is known to be NP-complete. In this paper we present two polyn…

math.CO2014★ 1 cited

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…

math.CO2013★ 16 cited

Permutations sortable by two stacks in parallel and quarter plane walks

Michael Albert, Mireille Bousquet-Mélou

At the end of the 1960s, Knuth characterised the permutations that can be sorted using a stack in terms of forbidden patterns. He also showed that they are in bijection with Dyck p…

math.CO2013★ 1 cited

Generating and enumerating 321-avoiding and skew-merged simple permutations

Michael H. Albert, Vincent Vatter

The simple permutations in two permutation classes --- the 321-avoiding permutations and the skew-merged permutations --- are enumerated using a uniform method. In both cases, thes…

math.CO2013★ 1 cited

Enumerating indices of Schubert varieties defined by inclusions

Michael H. Albert, Robert Brignall

By extending the notion of grid classes to include infinite grids, we establish a structural characterisation of the simple permutations in Av(4231, 35142, 42513, 351624), a patter…

math.CO2012

The enumeration of three pattern classes

M. H. Albert, M. D. Atkinson, Robert Brignall

The structure of three pattern classes Av(2143, 4321), Av(2143, 4312) and Av(1324, 4312) is determined using the machinery of monotone grid classes. This allows the permutations in…

math.CO2012★ 5 cited

Inflations of geometric grid classes of permutations

Michael H. Albert, Nik Ruskuc, Vincent Vatter

Geometric grid classes and the substitution decomposition have both been shown to be fundamental in the understanding of the structure of permutation classes. In particular, these…

math.CO2011★ 31 cited

On some fundamental results about higher-rank graphs and their C*-algebras

Robert Hazlewood, Iain Raeburn, Aidan Sims +1

Results of Fowler and Sims show that every k-graph is completely determined by its k-coloured skeleton and collection of commuting squares. Here we give an explicit description of…

math.CO2011★ 14 cited

The enumeration of permutations avoiding 2143 and 4231

Michael Albert, M. D. Atkinson, Robert Brignall

We enumerate the pattern class Av(2143,4231) and completely describe its permutations. The main tools are simple permutations and monotone grid classes.

math.CO2011★ 2 cited

Geometric grid classes of permutations

Michael H. Albert, M. D. Atkinson, Mathilde Bouvel +2

A geometric grid class consists of those permutations that can be drawn on a specified set of line segments of slope \pm1 arranged in a rectangular pattern governed by a matrix. Us…

math.CO2011★ 3 cited

Counting (3+1) - Avoiding permutations

M. D. Atkinson, Bruce E. Sagan, Vincent Vatter

A poset is {\it $(\3+\1)$-free} if it contains no induced subposet isomorphic to the disjoint union of a 3-element chain and a 1-element chain. These posets are of interest because…

math.CO2010

On the inverse image of pattern classes under bubble sort

Michael H. Albert, M. D. Atkinson, Mathilde Bouvel +2

Let B be the operation of re-ordering a sequence by one pass of bubble sort. We completely answer the question of when the inverse image of a principal pattern class under B is a p…

math.CO2010★ 1 cited

Young classes of permutations

Michael Albert

We characterise those classes of permutations having the property that for every tableau shape either every permutation of that shape or no permutation of that shape belongs to the…

math.CO2010★ 19 cited

Subclasses of the separable permutations

Michael H. Albert, M. D. Atkinson, Vincent Vatter

We prove that all subclasses of the separable permutations not containing Av(231) or a symmetry of this class have rational generating functions. Our principal tools are partial we…

math.CO2007★ 2 cited

The $p$ -modular descent algebras

M. D. Atkinson, G. Pfeiffer, S. J. van Willigenburg

The concept of descent algebras over a field of characteristic zero is extended to define descent algebras over a field of prime characteristic. Some basic algebraic structure of t…

math.CO2006★ 8 cited

Permutations Containing Many Patterns

M. H. Albert, Micah Coleman, Ryan Flynn +1

It is shown that the maximum number of patterns that can occur in a permutation of length $n$ is asymptotically $2^{n}$ . This significantly improves a previous result of Coleman.

math.CO2006

Permutation Classes of Polynomial Growth