13 citations · 30 across the 14 of their papers we have counts for
18 papers
Additivity of symmetric and subspace designs
Marco Buratti, Anamari Nakic
A - design is additive (or strongly additive) if it is possible to embed it in a suitable abelian group in such a way that its block set is contained in (or coincid…
Partitioned difference families and harmonious linear spaces
Marco Buratti, Dieter Jungnickel
We say that a linear space is harmonious if it is resolvable and admits an automorphism group acting sharply transitively on the points and transitively on the parallel classes. Ge…
Tight Heffter arrays from finite fields
Marco Buratti
After extending the classic notion of a tight Heffter array H to any group of order , we give direct constructions for elementary abelian tight Heffter arrays, hence…
Super-regular Steiner 2-designs
Marco Buratti, Anamari Nakić
A design is additive under an abelian group (briefly, -additive) if, up to isomorphism, its point set is contained in and the elements of each block sum up to zero. The…
Partitioned difference families: the storm has not yet passed
Marco Buratti, Dieter Jungnickel
Two years ago, we alarmed the scientific community about the large number of bad papers in the literature on {\it zero difference balanced functions}, where direct proofs of seemin…
The first families of highly symmetric Kirkman Triple Systems whose orders fill a congruence class
Simona Bonvicini, Marco Buratti, Martino Garonzi +2
Kirkman triple systems (KTSs) are among the most popular combinatorial designs and their existence has been settled a long time ago. Yet, in comparison with Steiner triple systems,…
New Results on Modular Golomb Rulers, Optical Orthogonal Codes and Related Structures
Marco Buratti, Douglas R. Stinson
We prove new existence and nonexistence results for modular Golomb rulers in this paper. We completely determine which modular Golomb rulers of order exist, for all ,…
On Resolvable Golomb Rulers, Symmetric Configurations and Progressive Dinner Parties
Marco Buratti, Douglas R. Stinson
We define a new type of Golomb ruler, which we term a resolvable Golomb ruler. These are Golomb rulers that satisfy an additional "resolvability" condition that allows them to gene…
Graph decompositions in projective geometries
Marco Buratti, Anamari Nakic, Alfred Wassermann
Let PG be the -dimensional projective space over and let be a simple graph of order for some . A 2 desig…
A reduction of the spectrum problem for odd sun systems and the prime case
Marco Buratti, Anita Pasotti, Tommaso Traetta
A -cycle with a pendant edge attached to each vertex is called a -sun. The existence problem for -sun decompositions of , with odd, has been solved only when $k=3…
Merging Combinatorial Design and Optimization: the Oberwolfach Problem
Fabio Salassa, Gabriele Dragotto, Tommaso Traetta +2
The Oberwolfach Problem -- posed by Gerhard Ringel in 1967 -- is a paradigmatic Combinatorial Design problem asking whether the complete graph decomposes into edge-di…
Designs over finite fields by difference methods
Marco Buratti, Anamari Nakic
One of the very first results about designs over finite fields, by S. Thomas, is the existence of a cyclic 2- design over for every integer coprime wi…
-analogs of group divisible designs
Marco Buratti, Michael Kiermaier, Sascha Kurz +2
A well known class of objects in combinatorial design theory are {group divisible designs}. Here, we introduce the -analogs of group divisible designs. It turns out that there a…
Fano Kaleidoscopes and their generalizations
Marco Buratti, Francesca Merola
In this work we introduce Fano Kaleidoscopes, Hesse Kaleidoscopes and their generalizations. These are a particular kind of colored designs for which we will discuss general theory…
On disjoint difference families
Marco Buratti
A disjoint difference family in an additive group is a partition of into sets of size whose lists of differences cover, altogether, every non-…
Hadamard partitioned difference families and their descendants
Marco Buratti
If is a Hadamard difference set (HDS) in , then is clearly a partitioned difference family (PDF). An…
Octahedral, dicyclic and special linear solutions of some unsolved Hamilton-Waterloo problems
Simona Bonvicini, Marco Buratti
We give a sharply-vertex-transitive solution of each of the nine Hamilton-Waterloo problems left open by Danziger, Quattrocchi and Stevens.
On the full automorphism group of a Hamiltonian cycle system of odd order
Marco Buratti, Graham J. Lovegrove, Tommaso Traetta
It is shown that a necessary condition for an abstract group G to be the full automorphism group of a Hamiltonian cycle system is that G has odd order or it is either binary, or th…