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Mark Dukes

Lecturer/Assistant Professor

School Of Mathematics & Statistics
Science Centre - South
Belfield
Dublin 4

Tel: +353 1 7162592
Email: mark.dukes@ucd.ie

Biography

Current Appointments:
Lecturer (above the bar), School of Mathematics & Statistics, University College Dublin, 2016-Present
Honorary Senior Lecturer, University of Strathclyde, 2016-Present

Previous Appointments:
Senior Lecturer, University of Strathclyde, 2011-2016
Research Scientist, University of Iceland, 2007-2011
Lecturer, University College Dublin, 2005-2007
Post-doctoral Fellow, University of Bordeaux 1, 2004-2005
Post-doctoral Fellow, University of Rome 2, 2003-2004
Post-doctoral Scholar, Dublin Institute for Advanced Studies, 2000-2003

Degrees:
PhD (Mathematics), Trinity College Dublin, 1997-2000
BA (Mathematical Sciences), University of Oxford, 1994-1997

Current Grants:

Principal Investigator on EPSRC grant: New combinatorial perspectives on the abelian sandpile model. £354,282. Grant reference: EP/M015874/1. (Ownership transferred to E. Steingrímsson on 23/9/2016 upon departing the UK.) June 2015 - June 2018.

Previous Grants:

Co-Investigator on Icelandic Research Fund Excellence grant: Combinatorics on permutations and words.P.I.: E. Steingrímsson. Grant reference: 90038011-3. ISK 67,609,000. Jan 2009 - Jan 2012.

Faculty of Science Grant, University of Strathclyde. Amount: £11,000. Jan 2012 - Dec 2013.

Professional

 

Associations

Association: Higher Education Academy, UK, Function/Role: Fellow
       

Committees

Committee : Ph.D. committee for Francois Nunzi, University of Paris Diderot
Committee : Ph.D. committee for candidate Timothy Revell, University of Strathclyde
Committee : Ph.D. committee for candidate Ghalib Nassar, University of Haifa
Committee : Ph.D. committee member for candidate Morgan Harvey, University of Strathclyde
Committee : M.Sc. committee for candidate Orn Arnaldsson, University of Iceland
Committee : M.Sc. committee for candidate H. Gudmundsson, Reykjavik University
Committee : M.Sc. committee for candidate M. Hardarson, Reykjavik University
Committee : M.Sc. committee for candidate Sanja Lozic, University of Novi Sad
Committee : British Combinatorial Conference BCC2017
Committee : Permutation Patterns 2012 Conference
Committee : FPSAC 2011 Conference
     

Consultancy

Client: EPSRC, UK
Client: National Security Agency, USA
Client: Icelandic Research Fund, Iceland

Outreach Activities

  • Irish Mathematical Olympiad Round 1 and Round 2 lecturer 2005-2006 and 2006-2007
  • Irish Mathematical Olympiad Training Camp 2007 - Instructor
  • Observer A at International Mathematical Olympiad 2007
  • Icelandic Mathematical Olympiad team Instructor, 2008
  • Problem Selection Committee Member, Nordic Mathematical Contest, 2009
  • Coordinator (Combinatorics) for the Baltic Way Contest, 2010


Journals Edited

Advances In Applied Mathematics: Reviewer.
Annals Of Combinatorics: Reviewer.
Discrete Mathematics: Reviewer.
Electronic Journal Of Combinatorics: Reviewer.
European Journal Of Combinatorics: Reviewer.
Graphs And Combinatorics: Reviewer.
Theoretical Computer Science: Reviewer.
Journal Of Combinatorial Theory - Series A: Reviewer.
Journal Of Combinatorics: Reviewer.
Journal Of Integer Sequences: Reviewer.
Journal Of Statistical Planning And Inference: Reviewer.
Journal Of Statistical Physics: Reviewer.
Proceedings Of The American Mathematical Society: Reviewer.
Information Processing Letters: Reviewer.
 

Publications

 

Book Chapters

Dukes, M; Le Borgne, Y (2016) 'New aspects of the abelian sandpile model on graphs and their polynomials' In: Shi, Y; Dehmer, M; Li, X; Gutman, I (eds). Graph Polynomials. Boca Raton, FL: Chapman and Hall/CRC. [Details]

Edited Books

Anders Claesson, Mark Dukes, Sergey Kitaev, David Manlove, Kitty Meeks (Ed.). (2017) Surveys in Combinatorics 2017. Cambridge, UK: Cambridge University Press. [DOI] [Details]

Peer Reviewed Journals

Mark Dukes (2016) 'Generalized ballot sequences are ascent sequences'. Australasian Journal of Combinatorics, . Available Online [Details]
Dukes, M; Selig, T (2016) 'Decomposing recurrent states of the abelian sandpile model'. Electronic Notes in Discrete Mathematics, 54 :97-102. [Details]
Tom S. Weber, Mark Dukes, Denise C. Miles, Stefan P. Glaser, Shalin H. Naik, Ken R. Duffy (2016) 'Site-specific recombinatorics: in situ cellular barcoding with the Cre Lox system'. BMC Systems Biology, . [DOI] [Details]
Mark Dukes, Chris D White (2016) 'Web matrices: structural properties and generating combinatorial identities'. Electronic Journal of Combinatorics, . Available Online [Details]
Jean-Christophe Aval, Michele D'Adderio, Mark Dukes, Yvan Le Borgne (2016) 'Two operators on sandpile configurations, the sandpile model on the complete bipartite graph, and a Cyclic Lemma'. Advances in Applied Mathematics, . [DOI] [Details]
Jean-Christophe Aval, Michele D'Adderio, Mark Dukes, Angela Hicks, Yvan Le Borgne (2014) 'Statistics on parallelogram polyominoes and a q,tq,t-analogue of the Narayana numbers'. Journal of Combinatorial Theory - Series A, . [DOI] [Details]
Mark Dukes (2014) 'Revstack sort, zigzag patterns, descent polynomials of t-revstack sortable permutations, and Steingrímsson's sorting conjecture'. Electronic Journal of Combinatorics, . Available Online [Details]
Mark Dukes, Einan Gardi, Heather McAslan, Darren J. Scott, Chris D. White (2014) 'Webs and posets'. Journal of High Energy Physics, . [DOI] [Details]
Mark Dukes, Yvan Le Borgne (2013) 'Parallelogram polyominoes, the sandpile model on a complete bipartite graph, and a q,t-Narayana polynomial'. Journal of Combinatorial Theory - Series A, . [DOI] [Details]
Jean-Christophe Aval, Michele d'Adderio, Mark Dukes, Angela Hicks, Yvan Le Borgne (2013) 'A q,t-analogue of Narayana numbers'. Discrete Mathematics and Theoretical Computer Science, . Available Online [Details]
Mark Dukes, Einan Gardi, Einar Steingrímsson, Chris D. White (2013) 'Web worlds, web-colouring matrices, and web-mixing matrices'. Journal of Combinatorial Theory - Series A, . [DOI] [Details]
Dukes, M; Jelinek, V; Kubitzke, M (2011) 'Composition matrices, (2+2)-free posets and their specializations'. Electronic Journal of Combinatorics, 18 (1). [Details]
Dukes, M; Kitaev, S; Remmel, J; Steingrímsson, E (2011) 'Enumerating (2+2)-free posets by indistinguishable elements'. Journal of Combinatorics, 2 (1). [Details]
Albert, M; Atkinson, M; Bouvel, M; Claesson, M; Dukes, M (2011) 'On the inverse image of pattern classes under bubble sort'. Journal of Combinatorics, 2 . [Details]
Claesson, A; Dukes, M; Kitaev, S (2011) 'A direct encoding of Stoimenow's matchings as ascent sequences'. Australasian Journal of Combinatorics, 49 . [Details]
Claesson, A; Dukes, M; Kubitzke, M (2011) 'Partition and composition matrices'. Journal of Combinatorial Theory - Series A, 118 (5). [Details]
Chung, F; Claesson, A; Dukes, M; Graham, R (2010) 'Descent polynomials for permutations with bounded drop size'. European Journal of Combinatorics, 31 (7). [Details]
Claesson, A; Dukes, M; Steingrimsson, E (2010) 'Permutations sortable by n-4 passes through a stack'. Annals of Combinatorics, 14 . [Details]
Dukes, M; Reifegerste, A (2010) 'The area above the Dyck path of a permutation'. Advances in Applied Mathematics, 45 . [Details]
Dukes, M; Parviainen, R (2010) 'Ascent sequences and upper triangular matrices containing non-negative integers'. Electronic Journal of Combinatorics, 17 (1). [Details]
Bousquet-Melou, M; Claesson, A; Dukes, M; Kitaev, S (2010) '(2+2)-free posets, ascent sequences and pattern avoiding permutations'. Journal of Combinatorial Theory - Series A, 117 (7). [Details]
David, F; Dukes, M; Jonsson, T; Stefansson, S-O (2009) 'Random tree growth by vertex splitting'. Journal of Statistical Mechanics: Theory and Experiment, (4). [Details]
Dukes, WMB; Jelínek, V; Mansour, T; Reifegerste, A (2009) 'New equivalences for pattern avoidance for involutions'. Proceedings of the American Mathematical Society, 137 . [Details]
Deng, EYP; Dukes, WMB; Mansour, T; Wu, SYJ (2009) 'Symmetric Schröder paths and restricted involutions'. Discrete Mathematics, 309 . [Details]
Dukes, M (2008) 'Concerning the shape of a geometric lattice'. Discrete Mathematics, 308 . [Details]
Dukes, WMB; Flanagan, M; Mansour, T; Vajnovszki, V (2008) 'Combinatorial Gray codes for classes of pattern avoiding permutations'. Theoretical Computer Science, 396 . [Details]
Dukes, W; Mansour, T; Reifegerste, A (2008) 'Wilf classification of three and four letter signed patterns'. Discrete Mathematics, 308 . [Details]
M. Dukes; (2007) 'Permutation statistics on involutions'. European J. Combin, 28 :186-198. [Details]
M. Dukes, T. Mansour; (2007) 'Signed involutions avoiding 2-letter signed patterns'. Annals of Combinatorics, . [Details]
Dukes, M ;Duffy, K (2004) 'On Knuth's generalization of Banach's matchbox problem'. Mathematical Proceedings of the Royal Irish Academy, (104):107-118. [Details]
M. Dukes; (2004) 'On the number of matroids on a finite set'. Sém. Lothar. Combin, 51 . [Details]
M. Dukes, T. C. Dorlas; (2004) 'Fluctuations of the local magnetic field in frustrated mean-field Ising models'. Markov Processes and Related Fields, 10 :585-606. [Details]
M. Dukes; (2003) 'Bounds on the number of generalized partitions and some applications'. Australas. J. Comb, (28):257-262. [Details]
M. Dukes, T. C. Dorlas; (2002) 'Large deviation approach to the generalised random energy model'. J. Phys. A: Math. Gen, 35 :4385-4394. [Details]
M. Dukes; (2002) 'On a unimodality conjecture in matroid theory'. Discrete Math. Theor. Comput. Sci, :181-190. [Details]
 

Conference Publications

Dukes, M; Mansour, T (2007) Involutions avoiding the class of permutations in Sk with prefix 12 19th International Conference on Formal Power Series & Algebraic Combinatorics http://igm.univ-mlv.fr/~fpsac/FPSAC07/SITE07/, Available Online [Details]
Dukes, M; Jelínek, V; Mansour, T; Reifegerste, A (2008) Equivalences for pattern avoiding involutions and classification 20th International Conference on Formal Power Series & Algebraic Combinatorics Discrete Math. Theor. Comput. Sci. Proc. AJ, , pp.181-188 [Details]
Bousquet-Mélou, M; Claesson, A; Dukes, M; Kitaev, S (2009) Unlabeled (2+2)-free posets, ascent sequences and pattern avoiding permutations 21st International Conference on Formal Power Series & Algebraic Combinatorics 21st International Conference on Formal Power Series & Algebraic Combinatorics, , pp.216-228 [Details]
Chung, F; Claesson, A; Dukes, M; Graham, R (2010) Descent polynomials for permutations with bounded drop size 22nd International Conference on Formal Power Series & Algebraic Combinatorics Discrete Math. Theor. Comput. Sci. Proc. AN, , pp.247-258 [Details]
Claesson, A; Dukes, M; Kubitzke, M (2011) Partition and composition matrices: two matrix analogues of set partitions 23rd International Conference on Formal Power Series & Algebraic Combinatorics Discrete Math. Theor. Comput. Sci. Proc. AO, , pp.221-232 [Details]
Dukes, M; Le Borgne, Y (2012) The sandpile model on a bipartite graph, parallelogram polyominoes, and a q,t-Narayana polynomial 24th International Conference on Formal Power Series & Algebraic Combinatorics Discrete Math. Theor. Comput. Sci. Proc. AR, , pp.337-348 [Details]
Aval, J-C; d'Adderio, M; Dukes, M; Hicks, A; Le Borgne, Y (2013) A q,t-analogue of Narayana numbers 25th International Conference on Formal Power Series & Algebraic Combinatorics Discrete Math. Theor. Comput. Sci. Proc. AS, , pp.623-634 [Details]
                                                                                                                 

Research

Research Interests

My homepage containing information about my research and research interests can be found here
     

Teaching

 

Modules Coordinated

201600   MATH20270     Mathematics: Theory of Games
201600   MATH10210     Mathematics: Found. of Math. for Com.Sc. I
201600   MST30040     Mathematical Studies: Differential Equations
   

Developing as a Teacher

P.G. Certificate in Academic Studies (Academic Practice).
Fellow of the Higher Education Academy.
 

Collaborators

Internal Collaborators

Mark Flanagan, UCD, Ireland.

External Collaborators

Michael H. Albert, Otago, New Zealand.
Mike D. Atkinson, Otago, New Zealand.
Jean-Christophe Aval, Bordeaux, France.
Mireille Bousquet-Mélou, Bordeaux, France.
Mathilde Bouvel, Zurich, Switzerland.
Fan Chung, San Diego, USA.
Anders Claesson, Strathclyde, UK.
Michele D'Adderio, Brussels, Belgium.
François David, Paris, France.
Eva Y. P. Deng, Dalian, China.
Tony Dorlas, Dublin, Ireland.
Ken Duffy, Maynooth, Ireland.
Einan Gardi, Edinburgh, UK.
Stefan Glaser, Melbourne, Australia.
Ronald Graham, San Diego, USA.
Angela Hicks, Stanford, USA.
Vit Jelínek, Prague, Czech Republic.
Þórður Jónsson, Reykjavík, Iceland.
Sergey Kitaev, Strathclyde, UK.
Martina Kubitzke, Frankfurt, Germany.
Yvan Le Borgne, Bordeaux, France. 
Toufik Mansour, Haifa, Israel. 
Heather McAslan, Sussex, UK.
Denise Miles, Melbourne, Australia.
Shalin Naik, Melbourne, Australia.
Robert Parviainen, WGS Gaming, USA.
Astrid Reifegerste, Magdeburg, Germany. 
Jeffrey Remmel, San Diego, USA. 
Darren J. Scott, Durham, UK.
Sigurður Örn Stefánsson, Reykjavik, Iceland. 
Einar Steingrímsson, Strathclyde, UK. 
Vincent Vajnovszki, Dijon, France. 
Tom Weber, Maynooth, Ireland.
Chris D. White, Glasgow, UK. 
Susan Yi Jun Wu, Tianjin, China.