Research interests:
- Discrete Tomography
- Enumerative Combinatorics
- Tilings of the plane
- NP completeness theory
- Bidimensional languages
- Theory of words
Papers:
2008
S. Brocchi, A. Frosini, C. Picouleau
“Reconstruction of binary matrices under fixed size neighborhood constraints”
Theoretical Computer Science, Vol.406, Issue 1-2 43-54
A.Frosini, M. Nivat, S. Rinaldi
“Scanning Integer Matrices by means of Two Rectangular Windows”
Theoretical Computer Science, Vol. 406 1-2 90-96
A.Frosini, C.Picouleau, S.Rinaldi
“Reconstructing Binary Matrices with Neighborhood Constraints: an NP Hard Problem”
Lecture Notes in Computer Science, Vol. 4992, proceedings of 14th International Conference on Discrete Geometry for Computer Imagery, DGCI 08, 392-400
F.Disanto, A.Frosini, M.Poneti, S.Rinaldi
“Permutominides: enumeration and poset structures”
Pure Mathematics and Applications, proceedings of GASCOM ’08 - Génération Aléatoire de Structures Combinatoires (to appear)
A. Blondin Massé, S. Brlek, S. Labbé, A. Frosini, S. Rinaldi
“Reconstructing words from a fixed palindromic length sequence”
IFIP International Federation for Information Processing, Volume 273, proceedings of Fifth IFIP International Conference on Theoretical Computer Science; Giorgio Ausiello, Juhani Karhumaki,Giancarlo Mauri, Luke Ong; (Boston: Springer), pp. 101–114
2007
F.Disanto, A.Frosini, R.Pinzani, S.Rinaldi
“A Closed Formula for the Number of Convex Permutominoes”
The electronic Journal of Combinatorics Vol. 14(1)
A.Frosini, M.Nivat “Binary Matrices under the Microscope: A Tomographical Problem” Theoretical Computer Science, Vol. 370 201-217. G.Castiglione, A.Frosini, E.Munarini, A.Restivo, S.Rinaldi
“Combinatorial aspects of L-convex polyominoes”
European Journal of Combinatorics 28 1724-1741
G.Castiglione, A.Frosini, A.Restivo, S.Rinaldi
“Tomographical Aspects of L-Convex Polyominoes”
Pure Mathematics and Applications, Vol.18 3-4 239-256
E. Barcucci, A. Frosini, A. Kuba, A. Nagy, S. Rinaldi, M. Samal, and S. Zopf
“Emission Discrete Tomography” (book chapter)
Advances in Discrete Tomography and Its Applications, (G.Herman and A.Kuba Eds.) Birkhauser
S. Brunetti, M.C. Costa, A. Frosini, F. Jarray, and C. Picouleau
“Reconstruction of Binary Matrices under Adjacency Constraints” (book chapter)
Advances in Discrete Tomography and Its Applications, (G.Herman and A.Kuba Eds.) Birkhauser
2006
S. Brleck, A. Frosini, S. Rinaldi, L. Vuillon
“Tilings by translation: enumeration by a rational language approach”
The electronic Journal of Combinatorics, Vol. 13(1).
A.Frosini, S.Rinaldi
“On the Sequence A079500 and Its Combinatorial Interpretations”
Journal of Integer Sequences, Vol. 9 Art. 06.3.1.
A.Frosini, S.Rinaldi
“An object grammar for L-convex polyominoes”
Pure Mathematics and Applications, 17 1-2 pp.1-11
I.Fanti, A.Frosini, E.Grazzini, R.Pinzani, S.Rinaldi
“Polyominoes determined by permutations”
MathInfo 06 Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, Nancy, DMTCS proc. AG 381-390
A.Frosini, S.Rinaldi, “An object grammar for the class of L-convex polyominoes” local proceedings of GASCom and Bijective Combinatorics 2006 (5th edition), R.Pinzani and V.Vajnovszki (Eds.), 112-123.
2005
E. Barcucci, A. Frosini, S.Rinaldi
“An algorithm for the reconstruction of discrete sets from two projections in presence of absorption”
Discrete Applied Mathematics, Vol.151/1-3 21-35
A.Frosini, G.Simi
“The reconstruction of a subclass of domino tilings from two projections”
Discrete Applied Mathematics, Vol.151/1-3 154-168.
E. Barcucci, A. Frosini, S.Rinaldi
“On Directed-Convex Polyominoes in a Rectangle”
Discrete Mathematics, Vol. 298/1-3 62-78.
A.Frosini, M.Nivat, L.Vuillon
“An introduction to Periodical Discrete Sets from a tomographical perspective”
Theoretical Computer Science, Vol. 347/1-2 370-392.
G.Castiglione, A.Frosini, A.Restivo, S.Rinaldi
“Enumeration of L-convex polyominoes by rows and columns”
Theoretical Computer Science, Vol. 347/1-2 336-352.
F.De Carli, A.Frosini, S.Rinaldi, A.Sorbi
“Some remarks on tiling recognizable languages”
Pure Mathematics and Applications, Vol. 16, No. 1-2 69-80.
A.Frosini, M.Nivat
“On a tomographic equivalence between (0,1) matrices”
Pure Mathematics and Applications, Vol. 16, No. 3 251-265.
G.Castiglione, A.Frosini, A.Restivo, S.Rinaldi
“A Tomographical Characterization of L-Convex Polyominoes”
Lecture Notes in Computer Science, Vol. 3429, proceedings of 12th International Conference on Discrete Geometry for Computer Imagery, DGCI 2005, 115-125.
S.Brunetti, A.Frosini, C.Picouleau
“Reconstructing a binary matrix under timetabling constraints”
Electronic Notes in Discrete Mathematics, Vol. 20, Proceedings of the Workshop on Discrete Tomography and its Applications 2005, Gabor T. Herman and Attila Kuba (Eds.), 99-112.
E. Barcucci, A. Frosini, A.Kuba, S.Rinaldi
“An efficient algorithm for reconstructing binary matrices from horizontal and vertical absorbed projections”
Electronic Notes in Discrete Mathematics, Vol. 20, Proceedings of the Workshop on Discrete Tomography and its Applications 2005, Gabor T. Herman and Attila Kuba (Eds.), 347-363.
G.Castiglione, A.Frosini, E.Munarini, A.Restivo, S.Rinaldi
“Enumeration of L-convex polyominoes. II. Bijection and area”
local proceedings of FPSAC 2005, #49, 531-541.
2004
A.Frosini, G.Simi
“The NP-completeness of a tomographical problem on bicolored domino tilings”
Theoretical Computer Science, Vol. 319/1-3 447-454.
A. Del Lungo, E.Duchi, A.Frosini, S.Rinaldi
“On the generation and enumeration of some classes of convex polyominoes”
The Electronic Journal of Combinatorics, 11 #R60.
A.Frosini, M.Nivat
“Binary Matrices under the Microscope: A Tomographical Problem”
Lecture Notes in Computer Science, Vol. 3322, proceedings of 10th International Workshop on Combinatorial Image Analysis, IWCIA 2004, 1-22
2003
E.Duchi, A.Frosini, R.Pinzani, S.Rinaldi
“A note on rational succession rules”
Journal of Integer Sequences, Vol. 6, Issue 1, Article 03.1.7.
A.Del Lungo, E.Duchi, A.Frosini, S.Rinaldi
“Enumeration of convex polyominoes using the ECO method”
Discrete Mathematics and Theoretical Computer Science, AB, 103-116.
A.Frosini, M.Mirolli, S.Rinaldi
“On the enumeration of pseudo-parallelogram polyominoes”
Pure Mathematics and Applications, Vol.14, no.1-2, (2003) 21-33.
E. Barcucci, A. Frosini, S.Rinaldi
“ Reconstruction of discrete sets from two absorbed projection: an algorithm”
Electronic Notes in Discrete Mathematics, Vol.12, proceedings of 9th International Workshop on Combinatorial Image Analysis, IWCIA 2003.
A.Frosini, G.Simi
“Reconstruction of low-degree domino tilings”
Electronic Notes in Discrete Mathematics, Vol.12, proceedings of 9th International Workshop on Combinatorial Image Analysis, IWCIA 2003.
A.Del Lungo, A.Frosini, S.Rinaldi
“ECO method and the exhaustive generation of convex polyominoes”
Lecture Notes in Computer Science, proceedings of Discrete Mathematics and Theoretical Computer Science, 4th International Conference, DMTCS 2003, 129-140.
2002
A.Frosini, G.Simi
“The reconstruction of a bicolored domino tiling from two projections”
Lecture Notes in Computer Science, No. 2301, 136-144, Proceedings of the 10th International Conference, DGCI 2002, Bourdeaux - France, A. Braquelaire, J.-O. Lachaud, A. Vialard (Eds.).
E.Barcucci, A.Frosini, S.Rinaldi
“Direct-convex polyominoes: ECO method and bijective results”
Proceedings of Formal Power Series and Algebraic Combinatorics 2002, R.Brak, O.Foda, C.Greenhill, T.Guttman, A.Owczarek (Eds.), Melbourne, #9.
A.Del Lungo, A.Frosini, M.Nivat, L.Vuillon,
“Discrete Tomography: Reconstruction under periodicity constraints”
Lecture Notes in Computer Science, No.2380, 38-56, Proceedings of Automata, Languages and Programming, 29th International Colloquium, ICALP 2002, Malaga - Spain, P.Widmaier and F.Triguero Ruiz and R.Morales and M.Hennessy and S.Heidenbenz and R.Conejo (Eds.).
2001
E. Barcucci, A. Del Lungo, A. Frosini, S. Rinaldi
“A technology for reverse-engineering a combinatorial problem from a rational generating function”
Advances in Applied Mathematics 26, (2001) 129-153.
2000
E. Barcucci, A. Del Lungo, A. Frosini, S. Rinaldi
“From rational functions to regular languages”
Formal Power Series and Algebraic Combinatorics, (D.Krob, A.A. Mikhailev and A.V. Mikhailev Eds.) Springer 633-644.
A. Frosini,
“A note on $\Delta_2^0$ sets of the Cantor space”
Pure Mathematics and Applications, Vol.10, No.1, pp. 41-57.
A. Frosini, R. Pinzani, S. Rinaldi
“About half the middle binomial coefficient”
Pure Mathematics and Applications, Vol.11, no.3, 497-508.
A. Frosini, S. Rinaldi
“The complexity of the reconstruction of (r,h,v) from two projections and an approximation algorithm”
Pure Mathematics and Applications, Vol.11, no.3, (2000) 485-496.