Publications
Journal Papers
Polygon dissections and some generalizations of cluster complexes, Journal of Combinatorial Theory Series A 113, pp. 1189-1198, 2006.
(with C.A. Athanasiadis) On the enumeration of positive cells in generalized cluster complexes and Catalan hyperplane arrangements, Journal of Algebraic Combinatorics 23: pp. 355-375, 2006.
Faces of generalized cluster complexes and noncrossing partitions, SIAM Journal on Discrete Mathematics 22, pp. 15-30, 2008.
(with C.A. Athanasiadis) Shellablity and higher order cohen-Macaulay connectivity of generalized cluster complexes, Israel Journal of Mathematics 167, pp. 177-191, 2008.
(with S. Fishel and M. Vazirani) Counting Shi regions with a fixed separating wall, Annals of Combinatorics 17 (4): 671-693, 2013.
(with M.I. Karavelas and R. Seidel) Convex hulls of spheres and convex hulls of disjoint convex polytopes, Computational Geometry: Theory and Application 46 (6), pp. 615-630, 2013.
(with S. Fishel and M. Kallipoliti) Facets of the generalized cluster complex and regions in the extended Catalan arrangement of type A_n, Electronic Journal of Combinatorics, 20(4), pp. 7, 2013.
(with M.I. Karavelas and C. Konaxis) The maximum number of faces of the Minkowski sum of three convex polytopes, Journal of Computational Geometry, 6(1), pp. 21-74, 2015.
(with M.I. Karavelas) The maximum number of faces of the Minkowski sum of two convex polytopes, Discrete & Computational Geometry, 55(4), pp. 748-786, 2016.
(with M.I. Karavelas) A geometric approach for the upper bound theorem for Minkowski sums of convex polytopes, Discrete & Computational Geometry, 56, pp. 966-1017, 2016.
(with F. E. Brochero Martínez, T. Garefalakis, L. Reis) On the multiplicative order of the roots of bX^{q^r+1}-aX^q^r}+dX-c, Finite Fields and Applications, 47, pp. 33-45, 2017.
(with M. Kallipoliti) Bijections between generalized Catalan families of types A and C. Discrete Mathematics, 341(9), pp. 2448–2464, 2018.
(with M. Kallipoliti and R. Sulzgruber) Patterns in Shi tableaux and Dyck paths, Order 2021, arXiv:2006.06949 [math.CO] poster
(with C.A.Athanasiadis) Symmetric decompositions, triangulations and real-rootedness, Mathematika 67(4),840–859, 2021 slides
(with Henri Mühle) Refined Lattice Path Enumeration and Combinatorial Reciprocity, Enumerative Combinatorics and Applications 3:1 (2023) Article #S2R8
Conference Papers
(with S. Fishel and M. Vazirani) Counting Shi regions with a fixed separating wall, In Proceedings of FPSAC 2011, Discr. Math. Theoret. Comput. Science, (2011).
(with M.I. Karavelas) Convex hulls of spheres and convex hulls of convex polytopes lying on parallel hyperplanes, In Proceedings of the 27th Annual ACM Symposium on Computational Geometry (SCG'11), pages 397-496, Paris, France, June 13-15, 2011.
(with M.I. Karavelas) The maximum number of faces of the Minkowski sum of two convex polytopes, In Proceedings of 23rd Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'12), pages 11-28, Kyoto, Japan, January 17-19, 2012.
(with M.I. Karavelas and C. Konaxis) The maximum number of faces of the Minkowski sum of three convex polytopes. In Proceedings of the 29th Annual ACM Symposium on Computational Geometry (SCG'13), Rio de Janeiro, Brazil, June 17-20, 2013.
(with M.I. Karavelas) A geometric approach for the upper bound theorem for Minkowski sums of convex polytopes, In Proceedings of the 31st International Symposium on Computational Geometry (SoCG 2015), Eindhoven, The Netherlands, June 22-25, 2015.
(with M. Kallipoliti) Bijections of dominant regions in the m-Shi arrangements of type A, B and C, In Proceedings of FPSAC 2016, Discr. Math. Theoret. Comput. Science, (2015).
Submitted/Preprints
(with M.I. Karavelas) Tight lower bounds on the number of faces of the Minkowski sum of polytopes via the Cayley trick, arXiv:1112.1535v1 [cs.CG]
(Aram Dermenjian) Enumerating regions of Shi arrangements per Weyl Cone, arXiv:2309.01725 [math.CO]