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Article

Dukes, Mark and Selig, Thomas and Smith, Jason P. and Steingrímsson, Einar (2019) Permutation graphs and the Abelian sandpile model, tiered trees and non-ambiguous binary trees. The Electronic Journal of Combinatorics, 26 (3). P3.29. ISSN 1077-8926

Dukes, Mark and Selig, Thomas (2016) Decomposing recurrent states of the abelian sandpile model. Electronic Notes in Discrete Mathematics, 54C. pp. 97-102. ISSN 1571-0653

Weber, Tom S. and Dukes, Mark and Miles, Denise C. and Glaser, Stefan P. and Naik, Shalin H. and Duffy, Ken R. (2016) Site-specific recombinatorics : in situ cellular barcoding with the Cre Lox system. BMC Systems Biology, 10. 43. ISSN 1752-0509

Dukes, Mark and White, Chris D. (2016) Web matrices : structural properties and generating combinatorial identities. The Electronic Journal of Combinatorics, 23 (1). P1.45. ISSN 1077-8926

Aval, Jean-Christophe and D'Adderio, Michele and Dukes, Mark and Le Borgne, Yvan (2016) Two operators on sandpile configurations, the sandpile model on the complete bipartite graph, and a Cyclic Lemma. Advances in Applied Mathematics, 73. pp. 59-98. ISSN 0196-8858

Dukes, Mark (2016) Generalized ballot sequences are ascent sequences. Australasian Journal of Combinatorics, 64 (1). pp. 61-63. ISSN 1034-4942

Dukes, Mark (2014) Revstack sort, zigzag patterns, descent polynomials of t-revstack sortable permutations, and Steingrímsson's sorting conjecture. The Electronic Journal of Combinatorics, 21 (2). P2.2. ISSN 1077-8926

Aval, Jean-Christophe and D'Adderio, Michele and Dukes, Mark and Hicks, Angela and Le Borgne, Yvan (2014) Statistics on parallelogram polyominoes and a q,t-analogue of the Narayana numbers. Journal of Combinatorial Theory Series A, 123 (1). pp. 271-286. ISSN 0097-3165

Dukes, Mark and Gardi, Einan and McAslan, Heather and Scott, Darren and White, Chris D. (2014) Webs and posets. Journal of High Energy Physics, 2014 (1). 24. ISSN 1029-8479

Dukes, Mark and Le Borgne, Yvan (2013) Parallelogram polyominoes, the sandpile model on a complete bipartite graph, and a q,t-Narayana polynomial. Journal of Combinatorial Theory Series A, 120 (4). pp. 816-842. ISSN 0097-3165

Dukes, Mark and Gardi, Einan and Steingrimsson, Einar and White, Chris (2013) Web worlds, web-colouring matrices, and web-mixing matrices. Journal of Combinatorial Theory Series A, 120 (5). pp. 1012-1037. ISSN 0097-3165

Claesson, Anders and Dukes, Mark and Kubitzke, Martina (2011) Partition and composition matrices. Journal of Combinatorial Theory Series A, 118 (5). pp. 1624-1637.

Claesson, Anders and Dukes, Mark and Kitaev, Sergey (2011) A direct encoding of Stoimenow's matchings as ascent sequences. Australasian Journal of Combinatorics, 49. pp. 47-59.

Dukes, Mark and Jelínek, Vit and Kubitzke, Martina (2011) Composition matrices, (2+2)-free posets and their specializations. The Electronic Journal of Combinatorics, 18 (1). P44.

Dukes, Mark and Kitaev, Sergey and Remmel, Jeffrey and Steingrimsson, Einar (2011) Enumerating (2+2)-free posets by indistinguishable elements. Journal of Combinatorics, 2 (1). pp. 139-163.

Albert, Michael and Atkinson, Michael and Bouvel, Mathilde and Claesson, Anders and Dukes, Mark (2011) On the inverse image of pattern classes under bubble sort. Journal of Combinatorics, 2 (2). pp. 231-243. ISSN 2156-3527

Bousquet-Melou, Mireille and Claesson, Anders and Dukes, Mark and Kitaev, Sergey (2010) (2+2)-free posets, ascent sequences and pattern avoiding permutations. Journal of Combinatorial Theory Series A, 117 (7). pp. 884-909.

Chung, Fan and Claesson, Anders and Dukes, Mark and Graham, Ronald (2010) Descent polynomials for permutations with bounded drop size. European Journal of Combinatorics, 31 (7). pp. 1853-1867.

Dukes, Mark and Reifegerste, Astrid (2010) The area above the Dyck path of a permutation. Advances in Applied Mathematics, 45 (1). pp. 15-23. ISSN 0196-8858

Dukes, Mark and Parviainen, Robert (2010) Ascent sequences and upper triangular matrices containing non-negative integers. The Electronic Journal of Combinatorics, 17. R53.

Steingrimsson, Einar and Dukes, Mark and Claesson, Anders (2010) Permutations sortable by n-4 passes through a stack. Annals of Combinatorics, 14. pp. 45-51.

David, François and Dukes, Mark and Jónsson, Thordur and Stefánsson, Sigurdur Örn (2009) Random tree growth by vertex splitting. Journal of Statistical Mechanics: Theory and Experiment, 2009 (4). ISSN 1742-5468

Dukes, W.M.B. and Jelínek, Vit and Mansour, Toufik and Reifegerste, Astrid (2009) New equivalences for pattern avoidance for involutions. Proceedings of the American Mathematical Society, 137 (2). pp. 457-465. ISSN 0002-9939

Dukes, W.M.B. and Deng, Eva and Mansour, Toufik and Wu, Susan (2009) Symmetric Schröder paths and restricted involutions. Discrete Mathematics, 309 (12). pp. 4108-4115. ISSN 0012-365X

Dukes, W.M.B. (2008) Concerning the shape of a geometric lattice. Discrete Mathematics, 308 (24). p. 6632. ISSN 0012-365X

Dukes, W.M.B. and Mansour, Toufik and Reifegerste, Astrid (2008) Wilf classification of three and four letter signed patterns. Discrete Mathematics, 308 (15). p. 3125. ISSN 0012-365X

Dukes, W. M. B. and Flanagan, Mark and Mansour, Toufik and Vajnovszki, Vincent (2008) Combinatorial Gray codes for classes of pattern avoiding permutations. Theoretical Computer Science, 396 (1 - 3). 35 - 49. ISSN 0304-3975

Dukes, W.M.B. and Mansour, Toufik (2007) Signed involutions avoiding 2-letter signed patterns. Annals of Combinatorics, 11 (3-4). pp. 387-403. ISSN 0218-0006

Dukes, W.M.B. (2007) Permutation statistics on involutions. European Journal of Combinatorics, 28 (1). pp. 186-198. ISSN 0195-6698

Dukes, W.M.B. and Duffy, Ken (2004) On Knuth's generalization of Banach's matchbox problem. Mathematical Proceedings of the Royal Irish Academy, 104 (1). pp. 107-118. ISSN 2009-0021

Dukes, W.M.B. and Dorlas, Tony (2004) Fluctuations of the local magnetic field in frustrated mean-field Ising models. Markov Processes and Related Fields, 10 (4). pp. 585-606. ISSN 1024-2953

Dukes, W.M.B. (2004) On the number of matroids on a finite set. Séminaire Lotharingien de Combinatoire, 51. B51g. ISSN 1286-4889

Dukes, W. M. B. (2003) Bounds on the number of generalized partitions and some applications. Australasian Journal of Combinatorics, 28. pp. 257-262. ISSN 1034-4942

Dorlas, T C and Dukes, W M B (2002) Large deviation approach to the generalized random energy model. Journal of Physics A: Mathematical and Theoretical, 35 (20). pp. 4385-4394. ISSN 0305-4470

Dukes, W.M.B. (2002) On a unimodality conjecture in matroid theory. Discrete Mathematics and Theoretical Computer Science, 5 (1). pp. 181-190. ISSN 1365-8050

Book Section

Aval, Jean-Christophe and D'Adderio, Michele and Dukes, Mark and Hicks, Angela and Le Borgne, Yvan; (2013) A q,t-analogue of Narayana numbers. In: DMTCS Proceedings. Discrete Mathematics & Theoretical Computer Science, Nancy, France, pp. 623-634.

Dukes, Mark and Le Borgne, Yvan; (2012) The sandpile model on a bipartite graph, parallelogram polyominoes, and a q,t-Narayana polynomial. In: DMTCS Proceedings. Discrete Mathematics & Theoretical Computer Science, Nancy, France, pp. 337-348.

Claesson, Anders and Dukes, Mark and Kubitzke, Martina; (2011) Partition and composition matrices : two matrix analogues of set partitions. In: DMTCS Proceedings. Discrete Mathematics & Theoretical Computer Science, Nancy, France, pp. 221-232.

Chung, Fan and Claesson, Anders and Dukes, Mark and Graham, Ronald; (2010) Descent polynomials for permutations with bounded drop size. In: DMTCS Proceedings. Discrete Mathematics & Theoretical Computer Science, Nancy, France, pp. 247-258.

Dukes, Mark and Jelinek, Vıt and Mansour, Toufik and Reifegerste, Astrid; (2008) Equivalences for pattern avoiding involutions and classification. In: DMTCS Proceedings. Discrete Mathematics & Theoretical Computer Science, Nancy, France, pp. 181-188.

Conference or Workshop Item

Bousquet-Melou, Mireille and Claesson, Anders and Dukes, Mark and Kitaev, Sergey (2009) Unlabeled (2+2)-free posets, ascent sequences and pattern avoiding permutations. In: 21st International Conference on Formal Power Series & Algebraic Combinatorics, 2009-07-20 - 2009-07-24.

Dukes, W. M. B. and Mansour, Toufik (2007) Involutions avoiding the class of permutations in Sk with prefix 12. In: 19th International Conference on Formal Power Series & Algebraic Combinatorics, 2007-07-02 - 2007-07-06, Nankai University.