Strathclyde Combinatorics Group
Department of
Mathematics and Statistics, University of Strathclyde
Research
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The main
research interests of the group lie in aspects of enumerative, bijective,
algebraic and topological combinatorics, with applications to computer
science, physics and biology. Much of our work has focussed on patterns in
permutations and other combinatorial objects. Central to this area is concept
of a permutation class, which is a downset under the permutation containment
order. The study of these structures began in the 1960s with Donald Knuth’s
investigation of computational sorting devices, which is still an active area
of research. Subsequently, they have been used to analyse models of genome
rearrangement, the layout of integrated circuits, and gas models in
statistical physics, among other things. |
Who are we?
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Sergey Kitaev
(Head of Group)
Sergey’s
research interests encompass aspects of enumerative and algebraic
combinatorics, combinatorics on words, and graph theory. Successes include
the enumeration of (2+2)-free posets via an encoding of them as ascent
sequences. Sergey is the author of two monographs, one on patterns in
permutations and words, and the other on words and graphs. Recently, he has
pioneered the theory of word-representable graphs (a topic on the boundary of
graph theory and combinatorics on words, with roots in algebra), including
giving an effective characterization in terms of graph orientations. |
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David Bevan
David’s
research interests mainly concern enumerative and asymptotic questions,
particularly in relation to permutations. Achievements include an explicit
formula for the growth rate of grid classes of permutations, and a structural
characterisation of the class of permutations avoiding 1324 together with new
bounds on its growth rate. Current research topics include the evolution of
the random permutation (as the number of its inversions increases),
permutation limits at different scales, and enumerative and structural
questions concerning permutation grid classes. |
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Elizabeth
Dombi
Elizabeth’s
research background lies in combinatorial semigroup theory, the algebraic
theory of formal languages, and combinatorial optimization concerning edge
covering of grid graphs. More recently, she has started working on
subdivision-resilience of non-word-representable graphs. |
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Einar
Steingrímsson
Einar’s
research interests primarily concern algebraic combinatorics, particularly in
relation to permutation patterns, and with an emphasis on permutation
statistics. He pioneered the concept of a vincular pattern, which has since
been generalised further by the notion of a mesh pattern. A particular focus
has been on the topology and Möbius function of intervals in the poset of
permutations ordered by pattern containment. Other recent work has concerned
the Abelian sandpile model, and the introduction and analysis of new
combinatorial structures whose motivation comes from particle physics. |
Research
visitor
• Herman Z.
Q. Chen, Chongqing Normal University (2024 – 2025)
Current PhD
students
• Dan
Threlfall (from 2020)
• Noura
Alshammari (from 2021)
• Humaira Hameed
(from 2023)
• Mohammed
Alshammari (from 2024)
Past events
• Scottish Combinatorics
Meeting 2023, 22–23 May 2023
• 
— Virtual Workshop,
15–16 June 2021
• 26th British
Combinatorial Conference, 3–7 July 2017
• Permutation Patterns 2012,
11–15 July 2012
• FPSAC 2011, 13–17
June 2011
Research
funding
• Shortening
universal words and DNA sequence assembly (Sergey Kitaev, Leverhulme
Research Fellowship, 2023–2024)
• Connecting
physics models via permutations (Einar Steingrímsson, Leverhulme Research
Fellowship, 2018–2020)
• New
combinatorial perspectives on the Abelian sandpile model (Mark Dukes and
Einar Steingrímsson, EPSRC, 2015–2018)
• The
Möbius function of the poset of permutations (Einar Steingrímsson, EPSRC, 2015–2018)
• Finding structure in sets of permutations
(Anders Claesson, Icelandic Research Fund, 2014–2016)
• Combinatorics of permutations and
words (Einar Steingrímsson, Anders Claesson, Sergey Kitaev and Mark Dukes,
Icelandic Research Fund, 2009–2012)
History
• The Strathclyde Combinatorics Group
had its origins in Gothenburg, Sweden, then moved to Reykjavík,
Iceland, before coming to Glasgow, Scotland. Einar has written a history of
the group, published in Enumerative Combinatorics and
Applications.
Former
faculty members of the group
• Anders Claesson (2011–2016; now Professor at the University of Iceland,
Reykjavík)
• Mark
Dukes (2011–2016; now Associate Professor at
University College, Dublin)
Former
research associates
• Thomas
Selig (2015–2018; now
Assistant Professor at Xi'an Jiaotong-Liverpool
University, Suzhou, China)
• Jason Smith (2015–2018; now
Senior Lecturer at Nottingham Trent University)
Former PhD
students
• Kittitat Iamthong (2018–2021; now Lecturer at Suranaree
University of Technology)
Encoding graphs by
words and morphisms
• Marc Glen (2016–2019) On word-representability of polyomino
triangulations and crown graphs
• Jason Smith (2012–2015; now
Senior Lecturer at Nottingham Trent University) On the Möbius
function and topology of the permutation poset
• Stuart Hannah (2011–2015) Interval order enumeration