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Combinatorics, Discrete Mathematics

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Employment (2)

University College Dublin: Dublin, IE

2016-09-01 to present | Associate Proferssor (School of Mathematics and Statistics)
Employment
Source: Self-asserted source
Mark Dukes

University of Strathclyde: Glasgow, Glasgow, GB

2011-02-01 to 2016-08-31 | Senior Lecturer (Computer Science)
Employment
Source: Self-asserted source
Mark Dukes

Works (50 of 51)

Items per page:
Page 1 of 2

Parallelogram polyominoes and rectangular EW-tableaux: correspondences through the sandpile model

Enumerative Combinatorics and Applications
2021 | Journal article
Source: Self-asserted source
Mark Dukes

Refining the bijections among ascent sequences, (2+2)-free posets, integer matrices and pattern-avoiding permutations

Journal of Combinatorial Theory. Series A
2019 | Journal article
DOI: 10.1016/j.jcta.2019.05.007
EID:

2-s2.0-85066262582
Contributors: Dukes, M.; McNamara, P.R.W.
Source: Self-asserted source
Mark Dukes via Scopus - Elsevier

Refining the bijections among ascent sequences, (2+2)-free posets, integer matrices and pattern-avoiding permutations

Séminaire Lotharingien de Combinatoire
2019 | Conference paper
Source: Self-asserted source
Mark Dukes

The Abelian sandpile model on Ferrers graphs — A classification of recurrent configurations

European Journal of Combinatorics
2019 | Journal article
DOI: 10.1016/j.ejc.2019.05.008
EID:

2-s2.0-85067260076
Contributors: Dukes, M.; Selig, T.; Smith, J.P.; Steingrímsson, E.
Source: Self-asserted source
Mark Dukes via Scopus - Elsevier

Permutation graphs and the Abelian sandpile model, tiered trees and non-ambiguous binary trees

Electronic Journal of Combinatorics
2019-08-16 | Journal article
ARXIV: arXiv:1810.02437v1
Source: Self-asserted source
Mark Dukes

Decomposing recurrent states of the Abelian Sandpile Model

Séminaire Lotharingien de Combinatoire
2018 | Journal article
Source: Self-asserted source
Mark Dukes

Surveys in Combinatorics 2017
Source: Self-asserted source
Mark Dukes

Decomposing recurrent states of the abelian sandpile model

Electronic Notes in Discrete Mathematics
2016 | Journal article
DOI: 10.1016/j.endm.2016.09.018
EID:

2-s2.0-84992535709
Contributors: Dukes, M.; Selig, T.
Source: Self-asserted source
Mark Dukes via Scopus - Elsevier

Generalized ballot sequences are ascent sequences

Australasian Journal of Combinatorics
2016 | Journal article
EID:

2-s2.0-84946089849
Contributors: Dukes, M.
Source: Self-asserted source
Mark Dukes via Scopus - Elsevier

New aspects of the abelian sandpile model on graphs and their polynomials

Graph Polynomials
2016 | Book
Part of DOI: 10.1201/9781315367996
EID:

2-s2.0-85052700426
Contributors: Dukes, M.; Borgne, Y.L.
Source: Self-asserted source
Mark Dukes via Scopus - Elsevier

Site-specific recombinatorics: In situ cellular barcoding with the Cre Lox system

BMC Systems Biology
2016 | Journal article
DOI: 10.1186/s12918-016-0290-3
EID:

2-s2.0-84976878537
Contributors: Weber, T.S.; Dukes, M.; Miles, D.C.; Glaser, S.P.; Naik, S.H.; Duffy, K.R.
Source: Self-asserted source
Mark Dukes via Scopus - Elsevier

Two operators on sandpile configurations, the sandpile model on the complete bipartite graph, and a Cyclic Lemma

Advances in Applied Mathematics
2016 | Journal article
DOI: 10.1016/j.aam.2015.09.018
EID:

2-s2.0-84959419844
Contributors: Aval, J.-C.; D'Adderio, M.; Dukes, M.; Le Borgne, Y.
Source: Self-asserted source
Mark Dukes via Scopus - Elsevier

Web matrices: Structural properties and generating combinatorial identities

Electronic Journal of Combinatorics
2016 | Journal article
EID:

2-s2.0-84960114891
Contributors: Dukes, M.; White, C.D.
Source: Self-asserted source
Mark Dukes via Scopus - Elsevier

Web matrices: structural properties and generating combinatorial identities

Electronic Journal of Combinatorics
2016-03-04 | Journal article
ARXIV: 1603.01589
Source: Self-asserted source
Mark Dukes

Revstack sort, zigzag patterns, descent polynomials of t-revstack sortable permutations, and Steingrímsson's sorting conjecture

Electronic Journal of Combinatorics
2014 | Journal article
EID:

2-s2.0-84897468771
Contributors: Dukes, M.
Source: Self-asserted source
Mark Dukes via Scopus - Elsevier

Statistics on parallelogram polyominoes and a q, t-analogue of the Narayana numbers

Journal of Combinatorial Theory. Series A
2014 | Journal article
DOI: 10.1016/j.jcta.2013.09.001
EID:

2-s2.0-84893018364
Contributors: Aval, J.-C.; D'Adderio, M.; Dukes, M.; Hicks, A.; Le Borgne, Y.
Source: Self-asserted source
Mark Dukes via Scopus - Elsevier

Webs and posets

Journal of High Energy Physics
2014 | Journal article
DOI: 10.1007/Jhep01(2014)024
EID:

2-s2.0-84892392764
Contributors: Dukes, M.; Gardi, E.; McAslan, H.; Scott, D.J.; White, C.D.
Source: Self-asserted source
Mark Dukes via Scopus - Elsevier

Revstack sort, zigzag patterns, descent polynomials of t-revstack sortable permutations, and Steingrímsson's sorting conjecture

Electronic Journal of Combinatorics
2014-04-01 | Journal article
ARXIV: 1404.1457
Source: Self-asserted source
Mark Dukes

A q, t-analogue of Narayana numbers

Discrete Mathematics and Theoretical Computer Science
2013 | Journal article
EID:

2-s2.0-84887498551
Contributors: Aval, J.-C.; D'Adderio, M.; Dukes, M.; Hicks, A.; Le Borgne, Y.
Source: Self-asserted source
Mark Dukes via Scopus - Elsevier

Parallelogram polyominoes, the sandpile model on a complete bipartite graph, and a q, t-Narayana polynomial

Journal of Combinatorial Theory. Series A
2013 | Journal article
DOI: 10.1016/j.jcta.2013.01.004
EID:

2-s2.0-84873251521
Contributors: Dukes, M.; Le Borgne, Y.
Source: Self-asserted source
Mark Dukes via Scopus - Elsevier

Web worlds, web-colouring matrices, and web-mixing matrices

Journal of Combinatorial Theory. Series A
2013 | Journal article
DOI: 10.1016/j.jcta.2013.02.001
EID:

2-s2.0-84874348386
Contributors: Dukes, M.; Gardi, E.; Steingrímsson, E.; White, C.D.
Source: Self-asserted source
Mark Dukes via Scopus - Elsevier

The sandpile model on a bipartite graph, parallelogram polyominoes, and a q,t-Narayana polynomial

Discrete Mathematics and Theoretical Computer Science
2012 | Journal article
EID:

2-s2.0-84887545226
Contributors: Dukes, M.; Le Borgne, Y.
Source: Self-asserted source
Mark Dukes via Scopus - Elsevier

A direct encoding of stoimenow's matchings as ascent sequences

Australasian Journal of Combinatorics
2011 | Journal article
EID:

2-s2.0-79956275119
Contributors: Claesson, A.; Dukes, M.; Kitaev, S.
Source: Self-asserted source
Mark Dukes via Scopus - Elsevier

Composition matrices, (2 + 2)-free posets and their specializations

Electronic Journal of Combinatorics
2011 | Journal article
EID:

2-s2.0-79952964792
Contributors: Dukes, M.; Jelínek, V.; Kubitzke, M.
Source: Self-asserted source
Mark Dukes via Scopus - Elsevier

Enumerating (2+2)-free posets by indistinguishable elements

Journal of Combinatorics
2011 | Journal article
Source: Self-asserted source
Mark Dukes

On the inverse image of pattern classes under bubble sort

Journal of Combinatorics
2011 | Journal article
Source: Self-asserted source
Mark Dukes

Partition and composition matrices

Journal of Combinatorial Theory. Series A
2011 | Journal article
DOI: 10.1016/j.jcta.2011.02.001
EID:

2-s2.0-79951982755
Contributors: Claesson, A.; Dukes, M.; Kubitzke, M.
Source: Self-asserted source
Mark Dukes via Scopus - Elsevier

Partition and composition matrices: Two matrix analogues of set partitions

FPSAC'11 - 23rd International Conference on Formal Power Series and Algebraic Combinatorics
2011 | Conference paper
EID:

2-s2.0-84860471240
Contributors: Claesson, A.; Dukes, M.; Kubitzke, M.
Source: Self-asserted source
Mark Dukes via Scopus - Elsevier

(2+2)-free posets, ascent sequences and pattern avoiding permutations

Journal of Combinatorial Theory. Series A
2010 | Journal article
DOI: 10.1016/j.jcta.2009.12.007
EID:

2-s2.0-77953811550
Contributors: Bousquet-Mélou, M.; Claesson, A.; Dukes, M.; Kitaev, S.
Source: Self-asserted source
Mark Dukes via Scopus - Elsevier

Ascent sequences and upper triangular matrices containing non-negative integers

Electronic Journal of Combinatorics
2010 | Journal article
EID:

2-s2.0-77955692638
Contributors: Dukes, M.; Parviainen, R.
Source: Self-asserted source
Mark Dukes via Scopus - Elsevier

Descent polynomials for permutations with bounded drop size

European Journal of Combinatorics
2010 | Journal article
DOI: 10.1016/j.ejc.2010.01.011
EID:

2-s2.0-77955315365
Contributors: Chung, F.; Claesson, A.; Dukes, M.; Graham, R.
Source: Self-asserted source
Mark Dukes via Scopus - Elsevier

Descent polynomials for permutations with bounded drop size

FPSAC'10 - 22nd International Conference on Formal Power Series and Algebraic Combinatorics
2010 | Conference paper
EID:

2-s2.0-84860537718
Contributors: Chung, F.; Claesson, A.; Dukes, M.; Graham, R.
Source: Self-asserted source
Mark Dukes via Scopus - Elsevier

Permutations sortable by n - 4 passes through a stack

Annals of Combinatorics
2010 | Journal article
DOI: 10.1007/s00026-010-0044-7
EID:

2-s2.0-77949422873
Contributors: Claesson, A.; Dukes, M.; Steingrímsson, E.
Source: Self-asserted source
Mark Dukes via Scopus - Elsevier

The area above the Dyck path of a permutation

Advances in Applied Mathematics
2010 | Journal article
DOI: 10.1016/j.aam.2009.11.008
EID:

2-s2.0-77950369583
Contributors: Dukes, M.; Reifegerste, A.
Source: Self-asserted source
Mark Dukes via Scopus - Elsevier

New equivalences for pattern avoiding involutions

Proceedings of the American Mathematical Society
2009 | Journal article
DOI: 10.1090/S0002-9939-08-09492-6
EID:

2-s2.0-77950547519
Contributors: Dukes, W.M.B.; Jelínek, V.; Mansour, T.; Reifegerste, A.
Source: Self-asserted source
Mark Dukes via Scopus - Elsevier

Random tree growth by vertex splitting

Journal of Statistical Mechanics: Theory and Experiment
2009 | Journal article
DOI: 10.1088/1742-5468/2009/04/P04009
EID:

2-s2.0-70449365154
Contributors: David, F.; Dukes, W.M.B.; Jonsson, T.; Stefánsson, S.Ö.
Source: Self-asserted source
Mark Dukes via Scopus - Elsevier

Symmetric Schröder paths and restricted involutions

Discrete Mathematics
2009 | Journal article
DOI: 10.1016/j.disc.2008.12.011
EID:

2-s2.0-67349205090
Contributors: Deng, E.Y.P.; Dukes, M.; Mansour, T.; Wu, S.Y.J.
Source: Self-asserted source
Mark Dukes via Scopus - Elsevier

Unlabeled (2 + 2)-free posets, ascent sequences and pattern avoiding permutations

FPSAC'09 - 21st International Conference on Formal Power Series and Algebraic Combinatorics
2009 | Conference paper
EID:

2-s2.0-84860446356
Contributors: Bousquet-Mélou, M.; Claesson, A.; Dukes, M.; Kitaev, S.
Source: Self-asserted source
Mark Dukes via Scopus - Elsevier

Combinatorial Gray codes for classes of pattern avoiding permutations

Theoretical Computer Science
2008 | Journal article
DOI: 10.1016/j.tcs.2007.12.002
EID:

2-s2.0-42149153390
Contributors: Dukes, W.M.B.; Flanagan, M.F.; Mansour, T.; Vajnovszki, V.
Source: Self-asserted source
Mark Dukes via Scopus - Elsevier

Concerning the shape of a geometric lattice

Discrete Mathematics
2008 | Journal article
DOI: 10.1016/j.disc.2007.11.009
EID:

2-s2.0-56649117638
Contributors: Dukes, W.M.B.
Source: Self-asserted source
Mark Dukes via Scopus - Elsevier

Equivalences for pattern avoiding involutions and classification

FPSAC'08 - 20th International Conference on Formal Power Series and Algebraic Combinatorics
2008 | Conference paper
EID:

2-s2.0-84860429417
Contributors: Dukes, M.; Jelínek, V.; Mansour, T.; Reifegerste, A.
Source: Self-asserted source
Mark Dukes via Scopus - Elsevier

Wilf classification of three and four letter signed patterns

Discrete Mathematics
2008 | Journal article
DOI: 10.1016/j.disc.2007.06.013
EID:

2-s2.0-43249106499
Contributors: Dukes, W.M.B.; Mansour, T.; Reifegerste, A.
Source: Self-asserted source
Mark Dukes via Scopus - Elsevier

Involutions avoiding the class of permutations in S <inf>κ</inf> with prefix 12

FPSAC'07 - 19th International Conference on Formal Power Series and Algebraic Combinatorics
2007 | Conference paper
EID:

2-s2.0-84860758978
Contributors: Dukes, W.M.B.; Mansour, T.
Source: Self-asserted source
Mark Dukes via Scopus - Elsevier

Permutation statistics on involutions

European Journal of Combinatorics
2007 | Journal article
DOI: 10.1016/j.ejc.2005.07.014
EID:

2-s2.0-33748910835
Contributors: Dukes, W.M.B.
Source: Self-asserted source
Mark Dukes via Scopus - Elsevier

Signed involutions avoiding 2-letter signed patterns

Annals of Combinatorics
2007 | Journal article
DOI: 10.1007/s00026-007-0326-x
EID:

2-s2.0-43149100143
Contributors: Dukes, W.M.B.; Mansour, T.
Source: Self-asserted source
Mark Dukes via Scopus - Elsevier

On the number of matroids on a finite set

Séminaire Lotharingien de Combinatoire
2004 | Journal article
Source: Self-asserted source
Mark Dukes

On Knuth's generalization of Banach's matchbox problem

Mathematical Proceedings of the Royal Irish Academy
2004-11-01 | Journal article
Source: Self-asserted source
Mark Dukes

Fluctuations of the local magnetic field in frustrated mean-field Ising models

Markov Processes and Related Fields
2004-10-01 | Journal article
Source: Self-asserted source
Mark Dukes

Bounds on the number of generalized partitions and some applications

Australasian Journal of Combinatorics
2003 | Journal article
EID:

2-s2.0-84885932798
Contributors: Dukes, W.M.B.
Source: Self-asserted source
Mark Dukes via Scopus - Elsevier

Large deviation approach to the generalized random energy model

Journal of Physics A: Mathematical and General
2002 | Journal article
DOI: 10.1088/0305-4470/35/20/301
EID:

2-s2.0-0037166168
Contributors: Dorlas, T.C.; Dukes, W.M.B.
Source: Self-asserted source
Mark Dukes via Scopus - Elsevier
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