Combinatorial structures such as designs and Latin squares and their applications to cryptology.

RESEARCH INTERESTS

Combinatorial structures such as designs and Latin squares. In particular:

critical sets and defining sets
trades, in latin squares, block designs and graphs
Applications of combinatorics; for instance to cryptology
Visualisation of Energy Data and preprint

PUBLICATIONS

PREPRINTS

TO APPEAR

Nicholas Cavenagh, Diane Donovan, Abdollah Khodkar and G.H.J. van Rees, When is a partial latin square uniquely completable, but not its completable product? Discrete Mathematics, (to appear)

Nicholas Cavenagh, Diane Donovan and Abdollah Khodkar, Minimal defining sets of 1-factorizations of complete graphs, Utilitas Mathematica, (to appear)

Diane Donovan, Elizabeth J Billington and Nicole Smith, Packing a complete graph of order 5 (mod 6) with triangles: a new method, Bulletin of the ICA, (to appear)

Nicholas Cavenagh, Diane Donovan and Emine Sule Yazici, Minimal Homogeneous Steiner 2-(v,3) trades, Discrete Mathematics, (to appear)

Diane Donovan, James Lefevre and G.H.J. van Rees, On the spectrum of critical sets in latin squares of order 2ⁿ, Journal of Combinatorial Design, (to appear).

James Lefevre, Nicholas J Cavenagh, Diane Donovan and Ales Drapal, Minimal and minimum size latin bitrades of each genus, Commentationes Mathematicae Universitatis Carolinae, (to appear).

Nicholas Cavenagh, Diane Donovan, Abdollah Khodkar and G.H.J van Rees, When is a partial latin square uniquely completable, but not its completable product? Discrete Mathematics (to appear)

2007

Nicholas J Cavenagh, Diane Donovan and Rebecca A.H. Gower, A new class of critical sets for direct products of back circulant latin squares, Utilitas Mathematica,

Nicholas J Cavenagh, Diane M Donovan and Abdollah Khodkar, On the spectrum of Critical sets in back circulant latin squares, Ars Combinatoria .

2006

Nicholas J. Cavenagh, Diane Donovan and Emine Sule Yazici, Minimal homogeneous latin trades, Discrete Mathematics, 306 (2006), no. 17, 2047--2055.

Diane Donovan, Carlo Hamalainen and Anne Penfold Street, Seeking Solutions to Sudoku Squares, Pi in the Sky 10, (2006) 7-9 &11-12.

Birgit Loch and Diane Donovan, Progressive Teaching of Mathematics with Tablet Technology, e-Journal of Instructional Science and Technology (e-JIST), 9 , No. 2, (2006).

Diane Donovan, James Lefevre and Leonie Simpson, A discussion of constrained binary embeddings with applications to cryptanalysis of
irregularly clocked stream ciphers, Proceedings of International Conference on Discrete Mathematics (ICDM 2006), 75-87, Indian
Institute of Science, Bangalore, India, 12/06.

Igor Vladimirov, Diane Donovan, Bevan Thompson, Gibbs equilibrium in interacting particle systems with coordination constrained bonding on Bethe lattices, Proceedings of the Seventeenth Australasian Workshop on Combinatorial Algorithms (AWOCA2006), Ed. Ryan and Dafik, Uluru, July 16 -19, 2006, Ballarat University 110-122, ISBN 0-064-6463101.

2005

Nicholas J Cavenagh, Diane Donovan and Ales Drapal, 3-homogeneous latin trades, Discrete Mathematics, 300, (2005), no. 1-3, 57--70.

Nicholas J Cavenagh, Diane Donovan and Ales Drapal, 4-homogeneous latin trades, Australasian Journal of Combinatorics, 32 (2005), 285--303.

Nicholas J Cavenagh, Diane Donovan and Rebecca A.H. Gower, A new class of critical sets for direct products of backcirculant latin squares, Utilitas Mathematica, 67, (2005), 285--300.

Diane Donovan, Trevor Pickett and Richard Wilson, Visualising energy data, ANZIAM Journal (electronic supplement), Proceedings of the 2004 International conference on Computational Techniques and Applications, Melbourne, Australia, September 2004, (2005), C956--C970.

Nicholas J Cavenagh, Diane Donovan and Carlo Hamalainen, Are there three MOLS of order 10?, Proceedings of the Sixteenth Australasian Workshop on Combinatorial Algorithms (AWOCA2005), Eds. J Ryan, P Manyem, K Sugeng, M Miller, Ballarat, Australia, September 18--21, 2005, 57--65. ISBN 0-0646-45252-5

2004

Nicholas J. Cavenagh, Diane Donovan and G.H.J. van Rees,A note on the completion of partial latin squares, Proceedings of the Thirty-Fifth Southeastern International Conference on Combinatorics, Graph Theory and Computing. Congr. Numer. 168, (2004), 109--118.

Diane Donovan and Abdollah Khodkar, Uniform critical sets in Latin squares, J. Combin. Math. Combin. Computing, 48 (2004), 3--23 .Paper in PDF format

Nicholas J Cavenagh, Diane Donovan and Ales Drapal, Constructing and Deconstructing Latin Trades, Discrete Mathematics, 284 (2004) no.1-3, 97--105

Diane Donovan, Chin-Mei Fu and Abdollah Khodkar, An investigation of 2-critical sets in latin squares, Ars Combinatoria, 72 (2004), 223-234. Paper in PDF format

Diane Donovan, Saad El-Zanati, Charles Vanden Eynden and Somporn Sutinuntopas, Labelling of unions of up to four uniform cycles, Australasian Journal of Combinatorics, 29, (2004), 323--336.

Nicholas J Cavenagh, Carlo Hamalainen, Diane Donovan and Abdollah Khodkar, On Greedy Critical Sets in Latin Squares, Proceedings of the Fifteenth Australasian Workshop on Combinatorial Algorithms (AWOCA2004), Eds. Seok-Hee Hong, University of Sydney, 2004, 1157--163.

Diane Donovan, Trevor Pickett and Richard Wilson, Visualising Energy Data, presented at 12th Biennial Computational Techniques and Applications Conference, Melbourne, September 2004

2003
Diane Donovan and E.S.\ Mahmoodian, An algorithm for writing latin interchanges as the sum of intercalates, Bull. Inst. Combin. Applications, 34 (2002), 90--98. (Correction to a paper on critical sets: "An algorithm for writing any Latin interchange as a sum of intercalates" Bull. Inst. Combin. Appl. 37 (2003), 44.)

Diane Donovan and Abdollah Khodkar, Product constructions for critical sets in latin squares, 15th MCCCC (Las Vegas, NV, 2001). J. Combin. Math. Combin. Comput. 46 (2003), 227--254. Paper in PDF format

Diane Donovan, Abdollah Khodkar, Somporn Sutinuntopas and Siriwan Thappia ,A note on critical sets in latin squares of order 2^n-1, Congressus Numerantium 159 (2002), 215--219. 05B15

D.M. Donovan, E.S. Mahmoodian, C. Ramsay and A.P. Street, Defining sets in combinatorics: a survey, in Surveys in Combinatorics, 2003, Lecture Notes in Mathematics, Eds. C.D. Wensley Cambridge Uiversity Press, 2003, 115-174.

D.M. Donovan, A. Khodkar and A.P. Street, On minimal defining sets in AG(d,3), in Designs 2002: further combinatorial and constructive design theory, edited W.D. Wallis) Kluwer Academic Press, Boston, USA . Paper in PDF format

D.M. Donovan, A. Khodkar and A.P. Street, On doubling and tripling constructions for defining sets in Steiner triple systems, Graphs and Combinatorics, 19, 2003, 65 - 89 Paper in PDF format

D. Donovan, C. Iliopoulos, and M. Miller (eds.) Selected papers from 13th Australasian Workshop on Combinatorial Algorithms, Special Issue,
Journal of Automata, Languages and Combinatorics, Vol.8, Number 4, 2003, 555.

2002

Diane Donovan, Abdollah Khodkar, Somporn Sutinuntopas and Siriwan Thappia, A note on critical sets in Latin squares of order 2^ n-1,
Congr. Numer. 159, (2002), 215--219.

Diane Donovan and Abdollah Khodkar, Premature Partial Latin Squares and Critical Sets, Proceedings of the Thirteenth Austalasian Workshop on Combinatorial AlgorithmsAWOCA (2001), Eds. EJ Billington, D Donovan and A Khodkar, The Unviersity of Queensland, 2002, 119-129. Paper in PDF format

Bean, Richard; Donovan, Diane; Khodkar, Abdollah; Penfold Street, Anne Steiner trades that give rise to completely decomposable Latin interchanges. 11th Australasian Workshop on Combinatorial Algorithms (Hunter Valley, 2000). Int. J. Comput. Math. 79 (2002), no. 12, 1273--1284.

Diane Donovan and ES Mahmoodian, An algorithm for writing latin squares as the sum of intercalates, Bull. Inst. Combin. Applications, 34, 2002, 90--98. Correction Bull. Inst. Combin. Applications, 37, 2003, 44 Paper in PDF format

Diane Donovan, Rebecca A.H. Gower and Abdollah Khodkar, Latin interchanges and direct products, Ars Combinatoria, 64, 2002, 271-287.Paper in PDF format

2001

Diane Donovan, Chin-Mei Fu and Abdollah Khodkar, A discussion of 2-critical sets in Abelian 2-groups, Proceedings of the Twelth Austalasian Workshop on Combinatorial AlgorithmsAWOCA (2001), Eds. Edy Tri Baskoro, institut Teknologi, Bandung Indonesia, 2001, 88--97.Paper in PDF format

2000

Diane Donovan, Interactive discret mathematics, Proceedings of the Fourth Biennial International Conference of the Engineering Mathematics and Applications Conference EMAC 2000, Eds. R.L. May, G.F. Fitz-Gerald, I.H. Grundy, The Institute of Engineers, RMIT Melbourne, 2000, 131-133.Paper in PDF format

Richard Bean, Diane Donovan, Abdollah Khodkar and Anne Penfold Street, Steiner trades that give rise to completely decomposable latin interchanges, Proceedings of the Eleventh Australasian Workshop on Combinatorial AlgorithmsAWOCA 2000), Eds. L Brankovic and J Ryran, Newcastle University, Newcastle Aust., 2000, 17--30. Paper in PDF format

Diane Donovan, The completion of partial latin squares, Australasian Journal of Combinatorics, 22, 2000, 247-264.Paper in PDF format

Richard Bean and Diane Donovan, Closing a gap in the spectrum of critical sets, Australasian Journal of Combinatorics, 22, 2000, 191-200.Paper in PDF format

Diane Donovan and Adelle Howse, Towards the spectrum of critical sets, Australasian Journal of Combinatorics, 21, 2000, 107--130.Paper in PDF format

1999

Diane Donovan, Critical sets in Latin squares of order less than 11, J. Combin. Math. Combin. Computing, 29, 1999, 223--240.Paper in PDF format

1998

Diane Donovan, Critical sets in families of Latin squares, Utilitas Mathematica, 53, 1998, 3--16.Paper in PDF format

Diane Donovan and Adelle Howse, Critical sets in latin squares of order 7, J. Combin. Math. Combin. Computing, 28, 1998, 113--123.Paper in PDF format

Michael Bulmer, Diane Donovan, Catherine Holmes and Bevan Thompson, Calculus Connection, A Multimedia Adventure, Proceedings of the Third Biennial Australian Engineering Mathematics and A lications Conference EMAC '98, The Institute of Engineers, Adelaide, 1998, 147--150.

1997

Diane Donovan, Sheila Oates--Williams and Cheryl E. Praeger, On the distance between distinct group Latin squares, Journal of Combinatorial Design, 5, 1997, 235--245.Paper in PDF format

Diane Donovan, Adelle Howse and Peter Adams, A discussion of Latin interchanges, J. Combin. Math. Combin. Computing, 23, 1997, 161--182.Paper in PDF format

Diane Donovan, Secretly sharing passwords, The Australian Mathematics Teacher, 53, 1997, 21--25.Paper in PDF format

Diane Donovan and D.G. Hoffman, Critical sets in a family of groups, Australasian Journal of Combinatorics, 16, 1997, 21--28.Paper in PDF format

1996

Joan Cooper, Diane Donovan and Rebecca A.H. Gower, Critical sets in direct products of back circulant Latin squares, Utilitas Mathematica, 50, 1996, 127--162.

Diane Donovan and Joan Cooper, Critical sets in back circulant Latin squares, Aequationes Math., 52, 1996, 157--179.Paper in PDF format

Ed Dawson, Diane Donovan and Alan Offer, Quasigroups, isotopisms and authentication schemes, Australas. J. Combin., 13, 1996, 75--88.

Diane Donovan, Michael Lucht, M. Rezny, H. Sidhu, and H.B. Thompson, Interactive Maple tutorials, Australian Engineering Mathematics Conference `96AEMC96), Sydney, 1996, 499--503.

Diane Donovan and Paulette Lieby, Completely separating systems of k-sets for Latin squares, Proceeding of AWOCA `96, Magnetic Island, 1996, 47-56.

Diane Donovan, An update on Latin interchanges, Proceeding of AWOCA `96, Magnetic Island, 1996, 30--38.

1995

Diane Donovan, More a lications of mathematics in information security, Queensland Association of Mathematics Teachers' Conference, Gold Coast, September 1994, 24, 1996, 27--29.

Diane Donovan, Joan Cooper, D.J. Nott and Jennifer Seberry, Latin squares: critical sets and their lower bounds, Ars Combinatoria, 39, 1995, 33--48.

Diane Donovan, Key management systems and secret sharing schemes, Cryptography: Policy and Algorithms Conference, Brisbane, 1995, 369--380.

Diane Donovan, A lications of mathematics in information security, Queensland Association of Mathematics Teachers' Conference, Gold Coast, September 1994, in Teaching Mathematics, 20, 1995, 21--25.

1994

Joan Cooper, Diane Donovan and Jennifer Seberry, Secret sharing schemes arising from Latin squares, Bull. Inst. Combin. A lications, 12, 1994, 33--38.

Ed Dawson and Diane Donovan, The breadth of Shamir's scheme, Computers & Security, 13, 1994, 69--78.

Diane Donovan, Some interesting constructions for secret sharing schemes, Australas. J. Combin., 9, 1994, 37--66.

Joan Cooper and Diane Donovan, Latin interchanges, Proceedings of Sixteenth Australasian Workshop on Combinatorial Algorithms, Darwin, 1994, 29--35.

1984-93

Ed Dawson and Diane Donovan, Shamir's scheme says it all, Proc. Computer Security IFIP/Sec '93, Ed. E. Graham Dougall, Elesvier Science Publishers B.V., 1993, 91--102.

Diane Donovan and Alan Rahilly, The central spectrum of the order of a Steiner loop, Southeast Asian Bulletin of Mathematics, 16, 1992, 115--121.

E.P. Dawson, Diane Donovan and Alan Rahilly, Methods for sharing cryptographic keys, Communications '92, 1992, 135--139.

Diane Donovan and Sheila Oates--Williams, Single laws for sloops and squags, Discrete Math., 92, 1991, 79--83.

Rebecca A.H. Gower, Sheila Oates--Williams, Diane Donovan and Elizabeth J. Billington, The quasigroup variety arising from a 2-perfect 6-cycle system of order 13, J. Combin. Math. Combin. Computing, 10, 1991, 119--128.

Joan Cooper, Diane Donovan and Jennifer Seberry, Latin squares and critical sets of minimal size, Australas. J. Combin., 4, 1991, 113--120.

Diane Donovan, Single laws for two subvarieties of squags,Bull. Austral. Math. Soc., 42, 1990, 157--165.

Diane Donovan, The centre of a sloop, Australas. J. Combin., 1, 1990, 83--90.

Diane Donovan, Methods for constructing balanced ternary designs, Ars Combinatoria, 26B, 1988, 217--226.

Diane Donovan, More balanced ternary designs with block size four, J. Statist. Plann. Inference, 17, 1987, 109--133.

Diane Donovan, Balanced ternary designs with block size four, Ars Combinatoria, 21A, 1986, 81--88.

Diane Donovan, A family of balanced ternary designs with block size four, Bull. Austral. Math. Soc., 33, 1986, 321--327.

Diane Donovan, Balanced ternary designs from 1-designs, Ars Combinatoria, 19, 1985, 95--104.

Diane Donovan, The quiddity of the isomorphism classes of some balanced ternary designs: including some anomalies, Ars Combinatoria, 17A, 1984, 133--144.

BOOKS

E.J. Billington, B.D. Jones, S. Oates-Williams, A.P. Street, Discrete Mathematics: Logic and Structures, Longman Cheshire, Melbourne, 1990, 281+(x).

E.J. Billington, B.D. Jones, S. Oates-Williams, A.P. Street, Discrete Mathematics: Logic and Structures,2nd ed) Longman Cheshire, Melbourne, 1993, 316+(x).