Academic Experience

• 2006 to current: Full Professor of Geometry at the Faculty of Engineering of the University of Perugia, Italy
• 1999 till 2006: Associate Professor of Geometry at the Faculty of Engineering of the University of Perugia, Italy
• 1991 till 1999: Assistant Professor of Geometry at the Faculty of Engineering of the University of L'Aquila, Italy

Scientific interest

Constructions of combinatorial designs with a rich automorphism group

Citations

1324 citations by 490 documents; h-index 22 (Scopus, last update: August, 2019)

Education

1985. Master degree in Mathematics with excellence at the University La Sapienza of Rome

Awards

Hall Medal 1998 For outstanding contributions in Combinatorics and its Applications. Received at the University of Canterbury during the 17th British Combinatorial Conference (July, 1999)

Membership and Editorial Work

• Associate Editor of Discrete Mathematics since 2013
• Editor in chief of Bulletin of the Institute of Combinatorics and its Applications since 2016
• Member of U.M.I. (Unione Matematica Italiana) from 1992 to 2016
• Fellow of the Institute of Combinatorics and its Applications since 1994
• Council Member of the Institute of Combinatorics and its Applications since 2010
• Member of the Editorial Board of theJournal of Combinatorial Designs since 1999
• Member of the Editorial Board of theDesigns, Codes and Cryptography since 2017
• Member of the Editorial Board of theArt of Discrete Applied Mathematics since 2017

List of publications on international journals

• [98] F. Salassa, G. Dragotto, T. Traetta, M Buratti and F. Della Croce, Merging Combinatorial Design and Optimization: the Oberwolfach Problem, submitted
• [97] M. Buratti, A. Nakic and A. Wassermann, Graph decompositions over projective geometries, submitted
• [96] M. Buratti, Tiling rings with precious differences, submitted
• [95] M. Buratti, M. Kiermaier, S. Kurz, A. Nakic, and A. Wassermann, q-analogs of group divisible designs, submitted
• [94]M. Buratti and D. Jungnickel, Partitioned difference families versus Zero difference balanced functions, Designs, Codes and Cryptography, DOI: 10.1007/s10623-019-00632-x
• [93] M. Buratti, Hadamard partitioned difference families and their descendants, Cryptography and Communications 11 (2019), 557-562.
• [92] M. Buratti and A. Nakic, Designs over finite fields by difference methods, Finite Fields Appl. 57 (2019), 128-138.
• [91] M. Buratti and F. Merola, Fano Kaleidoscopes and their generalizations, Des. Codes Cryptogr. 87 (2019), 769-784.
• [90] M. Buratti, On disjoint (v, k, k-1) difference families, Des. Codes Cryptogr. 87 (2019), 745-755.
• [89] M. Buratti, On silver and golden optical orthogonal codes, Art Discrete Appl. Math. 1 (2018), #P2.02
• [88] M. Buratti and A. Wassermann, On decomposability of cyclic triple systems, Australas. J. Combin. 71 (2018), 184-195.
• [87] S. Bonvicini and M. Buratti, Octahedral, dicyclic and special linear solutions of some Hamilton-Waterloo problems, Ars Math. Contemp. 14 (2018), 1-14.
• [86] M. Buratti, H. Cao, D. Dai and T. Traetta, A complete solution to the existence of (k, λ)-cycle frames of type g^u, J. Combin. Des. 25 (2017), 197-230.
• [85] M. Buratti, G. Rinaldi and T. Traetta, 3-pyramidal Steiner triple systems, Ars Math. Contemp. 13 (2017), 95-106.
• [84] M. Buratti, S. Costa and X. Wang, New i-perfect cycle decompositions via vertex colorings of graphs, J. Combin. Des. 24 (2016), 495-513.
• [83] M. Buratti and P. Danziger, A cyclic solution for an infinite class of Hamilton-Waterloo problems, Graphs Combin. 32 (2016), 521-531.
• [82] M. Buratti, G.J. Lovegrove and T. Traetta, On the full automorphism group of a Hamiltonian cycle system of odd order, Graphs Combin. 31 (2015), 1855-1865.
• [81] M. Buratti and T. Traetta, The structure of 2-pyramidal 2-factorizations, Graphs Combin. 31 (2015), 523-535.
• [80] R.A. Bailey, M. Buratti, G. Rinaldi and T. Traetta, On 2-pyramidal Hamiltonian cycle systems, Bull. Belg. Math. Soc. Simon Stevin 21 (2014), 747-758.
• [79] M. Buratti and F. Merola, Hamiltonian cycle systems which are both cyclic and symmetric, J. Combin. Des 22 (2014), 367-390.
• [78] M. Buratti, G. Rinaldi and T. Traetta, Some results on 1-rotational Hamiltonian cycle systems, J. Combin. Des. 22 (2014), 231-251.
• [77] M. Buratti and A. Pasotti, Cyclic kite-designs of order v that are ciclically embedded into a cyclic (v,4,2)-design, Quaderni di Matematica.
• [76] M. Buratti, S. Capparelli, F. Merola, G. Rinaldi and T. Traetta, A collection of results on Hamiltonian cycle systems with a nice automorphism group, Electronic Notes in Discrete Mathematics 40 (2013), 245-252.
• [75] E.Brugnoli and M. Buratti, New designs by changing ... the signs, Electronic Notes in Discrete Mathematics 40 (2013) 49{52.
• [74] M. Buratti, A. Pasotti and D. Wu, On optimal (v,5,2,1) optical orthogonal codes, Des. Codes Cryptogr. 68 (2013), 349-371.
• [73] M. Buratti and F. Merola, Dihedral Hamiltonian cycle systems of the cocktail party graph, J. Combin. Des. 21 (2013), 1-23.
• [72] M. Buratti and T. Traetta, 2-starters, graceful labelings, and a doubling construction for the Oberwolfach Problem, J. Combin. Des. 20 (2012), 483-503.
• [71] S. Bonvicini, M. Buratti, G. Rinaldi and T. Traetta, Some progress on 1-rotational Steiner triple systems, Des. Codes Cryptogr. 62 (2012), 63-78.
• [70] M. Buratti, Y. Wei, D. Wu, P. Fan and M. Cheng, Relative difference families with variable block sizes and their related OOCs, IEEE Trans. Inform. Theory, 57 (2011), 7489-7497.
• [69] M. Buratti, K. Momihara and A. Pasotti, New results on optimal (v,4,2,1) optical orthogonal codes, Des. Codes Cryptogr. 58 (2011), 89-109.
• [68] M. Buratti, J. Yan and C. Wang, From a 1-rotational RBIBD to a partitioned difference family, Electronic J. Combin. 17 (2010).
• [67] M. Buratti, Difference families and Frobenius groups, RIMS Kokyuroku 1687 (2010), 71-76.
• [66] M. Buratti and D. Ghinelli, On disjoint (3t,3,1) difference families, J. Statist. Plann. Inference 140 (2010), 1918-1922.
• [65] M. Buratti, S. Capparelli and A. Del Fra, Cyclic Hamiltonian cycle systems of the λ-fold complete and cocktail party graphs, European J. Combin. 31 (2010), 1484-1496.
• [64] M. Buratti and A. Pasotti, Further progress on difference families with block size 4 or 5, Des. Codes Cryptogr. 56 (2010), 1-20.
• [63] M. Buratti and A. Pasotti, Combinatorial designs and the theorem of Weil on multiplicative character sums, Finite Fields Appl. 15 (2009), 332-344.
• [62] M. Buratti and G. Rinaldi, A non-existence result on cyclic cycle-decompositions of the cocktail party graph, Discrete Math. 309 (2009), 4722-4726.
• [61] K. Momihara and M. Buratti, Bounds and constructions of optimal (n, 4, 2, 1) optical orthogonal codes, IEEE Trans. Inform. Theory 55 (2009), 514-523.
• [60] M. Buratti, A. Bonisoli and G. Rinaldi, Sharply transitive decompositions of complete graphs into generalized Petersen graphs, Innov. Incidence Geom. 6/7 (2009), 95-109.
• [59] S.L. Wu and M. Buratti, A complete solution to the existence problem for 1-rotational k-cycle systems of K_v, J. Combin. Des. 17 (2009), 283-293.
• [58] M. Buratti and A. Pasotti, On perfect Γ-decompositions of the complete graph, J. Combin. Des. 17 (2009), 197-209.
• [57] M. Buratti and L. Gionfriddo, Strong difference families over arbitrary groups, J. Combin. Des. 16 (2008), 443-461.
• [56] M. Buratti and G. Rinaldi, 1-rotational k-factorizations of the complete graph and new solutions to the Oberwolfach problem, J. Combin. Des. 16 (2008), 87-100.
• [55] M. Buratti and N.J. Finizio, Existence results for 1-rotational resolvable Steiner 2-designs with block size 6 or 8, Bull. Inst. Combin. Appl. 50 (2007), 29-44.
• [54] M. Buratti, N.J. Finizio, M. Greig and B.J. Travers, Z-cyclic (t,8) GWhD(v), t=2,4, Util. Math. 72 (2007), 125-138.
• [53] A. Bonisoli, M. Buratti and G. Mazzuoccolo, Doubly transitive 2-factorizations, J. Combin. Des. 15 (2007), 120-132.
• [52] M. Buratti and A. Pasotti, Graph decompositions with the use of difference matrices, Bull. Inst. Combin. Appl. 47 (2006), 23-32.
• [51] M. Buratti, F. Rania and F. Zuanni, Some constructions for cyclic perfect cycle systems, Discrete Math. 299 (2005), 33-48.
• [50] M. Buratti and G. Rinaldi, On sharply vertex transitive 2-factorizations of the complete graph, J. Combin. Theory Ser. A 111 (2005), 245-256.
• [49] M. Buratti, Cycle decompositions with a sharply vertex transitive automorphism group, Matematiche (Catania) 59 (2004), 91-105.
• [48] M. Buratti and A. Del Fra, Cyclic Hamiltonian cycle systems of the complete graph, Discrete Math. 279 (2004), 107-119.
• [47] R.J.R. Abel and M. Buratti, Some progress on (v,4,1) difference families and optical orthogonal codes, J. Combin. Theory Ser. A 106 (2004), 59-75.
• [46] M. Buratti, Existence of 1-rotational k-cycle systems of the complete graph, Graphs Combin. 20 (2004), 41-46.
• [45] M. Buratti and A. Del Fra, Semi-Boolean Steiner quadruple systems and dimensional dual hyperovals, Adv. Geom. (2003), suppl., S254-S270.
• [44] M. Buratti, Rotational k-cycle systems of order v<3k; another proof of the existence of odd cycle systems, J. Combin. Des. 11 (2003), 433-441.
• [43] M. Buratti and A. Del Fra, A lower bound on the number of semi-Boolean quadruple systems, J. Combin. Des. 11 (2003), 229-239.
• [42] M. Buratti and A. Del Fra, Existence of cyclic k-cycle systems of the complete graph, Discrete Math. 261 (2003), 113-125.
• [41] M. Buratti, Constructions for resolved designs by difference methods, 6th Workshop on Combinatorics (Messina, 2002). Rend. Sem. Mat. Messina Ser. II 8(24) (2001/02), suppl., 19-28.
• [40] M. Buratti, Cyclic designs with block size 4 and related optimal optical orthogonal codes, Des. Codes Cryptogr. 26 (2002), 111-125.
• [39] M. Buratti, M. Gionfriddo, L. Milazzo and V. Voloshin, Lower and upper chromatic numbers for BSTSs(2^h-1), Computer Sci. J. Moldova 9 (2001), 259-272.
• [38] M. Buratti and F. Zuanni, Explicit constructions for 1-rotational Kirkman triple systems, Util. Math. 59 (2001), 27-30.
• [37] M. Buratti and F. Zuanni, Some observations on three classical BIBD constructions, Discrete Math. 283 (2001), 19-26.
• [36] M. Buratti, 1-rotational Steiner triple systems over arbitrary groups, J. Combin. Des. 9 (2001), 215-226.
• [35] R.J.R. Abel, M. Buratti, M. Greig and Y. Miao, Constructions for rotational near resolvable block designs, J. Combin. Des. 9 (2001), 157-181.
• [34] M. Buratti and F. Zuanni, Perfect Cayley Designs as generalizations of Perfect Mendelsohn Designs, Des. Codes Cryptogr. 23 (2001), 233-247.
• [33] M. Buratti, Abelian 1-factorizations of the complete graph, European J. Combin. 22 (2001), 291-295.
• [32] M. Buratti, Constructions for point-regular linear spaces, J. Statist. Plann. Inference 94 (2001), 139-146.
• [31] M. Buratti, Some regular Steiner 2-designs with block-size 4, Ars Combin. 55 (2000), 133-137.
• [30] M. Buratti, Two new classes of difference families, J. Combin. Theory Ser. A 90 (2000), 353-355.
• [29] M. Buratti, Existence of Z-cyclic triplewhist tournaments for a prime number of players, J. Combin. Theory Ser. A 90 (2000), 315-325.
• [28] M. Buratti and F. Zuanni, The 1-rotational Kirkman triple systems of order 33, J. Statist. Plann. Inference, 86/2 (2000), 369-377.
• [27] M. Buratti, Old and new designs via difference multisets and strong difference families, J. Combin. Des. 7 (1999), 406-425.
• [26] M. Buratti, Pairwise balanced designs from finite fields, Discrete Math. 208/209 (1999), 103-117.
• [25] M. Buratti and F. Zuanni, The 1-rotational (52,4,1)-RBIBD's, J. Combin. Math. Combin. Comput. 30 (1999), 99-102.
• [24] M. Buratti and F. Zuanni, On singular 1-rotational Steiner 2-designs, J. Comb. Theory Ser. A 86 (1999), 232-244.
• [23] M. Buratti, 1-rotational Kirkman triple systems generate dicyclic Steiner 2-designs with block-size 4, Bull. Inst. Combin. Appl. 26 (1999), 91-95.
• [22] M. Buratti, Some regular (17q,17,2) and (25q,25,3) BIBD constructions, Des. Codes Cryptogr. 16 (1999), 117-120.
• [21] M. Buratti and F. Zuanni, G-invariantly resolvable Steiner 2-designs which are 1-rotational over G, Bull. Belg. Math. Soc. 5 (1998), 221-235.
• [20] M. Buratti, Some constructions for 1-rotational BIBD's with block-size 5, Australas. J. Combin. 17 (1998), 199-227.
• [19] M. Buratti, Small quasimultiple of affine and projective planes; some improved bounds, J. Combin. Des. 6 (1998), 337-345.
• [18] M. Buratti, Recursive constructions for difference matrices and relative difference families, J. Combin. Des. 6 (1998), 165-182.
• [17] M. Buratti, Packing the blocks of a regular structure, Bull. Inst. Combin. Appl. 21 (1997), 49-58.
• [16] M. Buratti, Cyclotomic conditions leading to new Steiner 2-designs, Finite Fields Appl. 3 (1997), 300-313.
• [15] M. Buratti, G. Burosch and P.V. Ceccherini, A characterization of hypergraphs which are products of a finite number of edges, Rend. Mat. Appl. (7), Roma (1997), 373-385.
• [14] L. Berardi, M. Buratti and S. Innamorati, 4-blocked Hadamard 3-designs, Discrete Math. 174 (1997), 35-46.
• [13] M. Buratti, Clique-colourings characterizing Hamming graphs, Bull. Inst. Combin. Appl. 20 (1997), 57-61.
• [12] M. Buratti, On resolvable difference families, Des. Codes Cryptogr. 11 (1997), 11-23.
• [11] M. Buratti, From a (G,k,1) to a (C_k ⊕ G,k,1) difference family, Des. Codes Cryptogr. 11 (1997), 5-9.
• [10] M. Buratti, Edge-colourings characterizing a class of Cayley Graphs and a New Characterization of Hypercubes, Discrete Math. 161 (1996), 291-295.
• [9] M. Buratti, A packing problem and its application to Bose's families, J. Combin. Des. 4 (1996), 457-472.
• [8] M. Buratti, A powerful method for constructing difference families and optimal optical orthogonal codes, Des. Codes Cryptogr. 5 (1995), 13-25.
• [7] M. Buratti, Constructions of (q,k,1) difference families with q a prime power and k = 4,5, Discrete Math. 138 (1995), 169-175.
• [6] M. Buratti, On simple radical difference families, J. Combin. Des. 3 (1995), 161-168.
• [5] M. Buratti, Improving two theorems of Bose on difference families, J. Combin. Des. 3 (1995), 15-24.
• [4] M. Buratti, Cayley, Marty and Schreier Hypergraphs, Abh. Math. Sem. Univ. Hamburg 64 (1994), 151-162.
• [3] M. Buratti, Schubert Graphs, Symmetric Groups and Flags of Boolean Lattices, J. Geom. 48 (1993), 10-22.
• [2] M. Buratti, On a property of symmetric designs of order n ≡ 2 (mod 4), J. Geom. 34 (1989), 30-35.
• [1] M. Buratti, Bruck-Ryser Abstract Theorem and Symmetric Designs, Geom. Dedicata 27 (1988), 241-250.

Last update: September, 2019