John van Rees
Position:
Office:
E2-480 EITC
Department of Computer Science
University of Manitoba
Winnipeg, Manitoba
Canada R3T 2N2
(204)474-8683
Email:
vanrees[at]cs.umanitoba.ca
Table of Contents
1978 Ph.D. University of Waterloo (Combinatorics) 1974 M.Math University of Waterloo (Combinatorics) 1973 Teach. Cert. University of Western Ontario (Education) 1973 B. Math University of Waterloo (Combinatorics and Optimization)
07,2006-07,2009 Associate Head Department of Computer Science University of Manitoba 01,2003 - 07,2003 Acting Associate Head Dept. of Computer Science University of Manitoba 1995 - 1998 Associate Head Dept. of Computer Science University of Manitoba 1992 - Present Professor University of Manitoba 1982 - 1992 Associate Professor University of Manitoba 1985 Tenured University of Manitoba 1979 - 1982 Assistant Professor University of Manitoba 1978 - 1979 Assistant Professor Dalhousie University
I have been working to find instances of combinatorial configurations, especially balanced incomplete block designs, binary codes and covering designs. First, the necessary conditions are studied in the hope of tightening them. Second, computer algorithms are developed to find these designs not ruled out. A more recent interest is to develop these algorithms for a parallel machines. I also apply these configurations to lottery designs. I have developed a new interest in quantum computing.
National Sciences and Engineering Research Council (Maths B)
(2007 - 2012) total $60,000National Sciences and Engineering Research Council (Maths B)
(2002 - 2007) total $55,000National Sciences and Engineering Research Council (Maths B)
(1998 - 2002) total $40,000National Sciences and Engineering Research Council (Maths B)
(1994 - 1998) total $32,000National Sciences and Engineering Research Council (Maths Ctte)
(1991 - 1994) total $24,000University of Manitoba Grant - Aid of Research
(1990) $1,996National Sciences and Engineering Research Council (Maths Ctte)
(1988 - 1991) total $16,300National Sciences and Engineering Research Council (Maths Ctte)
(1985 - 1988) total $15,800University of Manitoba Grant - Aid of Research
(1983) $1,206National Sciences and Engineering Research Council (Maths Ctte)
(1982 - 1985) total $15,324National Sciences and Engineering Research Council (Maths Ctte)
(1979 - 1982) total $9,116 for 3 years
University of Newcastle Internal Research Assessment Ctte)
(1980) $1200University of Manitoba Grant - Aid of Research
(1979) $1,014University of Dalhousie Research Development Fund
(1978) $300
Doug Stinson 1 day August, 2009 Tian Zihong 1 week July, 2009 Navin Singhi 4 days July, 2009 R. Wei 2 days August, 2005 W. D. Wallis 3 day July, 2005 Alewyn Burger & Werner Grundlingh 3 days 2004 Richard Bean 2 days 2004 Nick Cavenagh 2 weeks 2002 Alan Ling 10 days 2002 Diane Donovan 2 weeks 2001 Clement Lam 1 week 2000 W.D.Wallis 4+4 days 1999 D. Stinson 1 week 1998 W.D.Wallis 1 week 1998 A. Ling 2 week 1997 L. Zhu 1 week 1997 E. Mahmoodian 2 months 1996 D. Stinson 1 year 1996 - 1997 A. Baarthmans 4 days 1995 W. Wallis 4 days 1995 D. Stinson 1 week 1995 D. Kreher 1 week 1993 D. Stinson several visits 1991 - 1993 R. Craigen 2 days M. Morley 2 weeks 1992 M. Greig 1 week 1990 Marshall Hall Jr. several visits 1986 - 1989
Nineteenth Midwest Conference on Combinatorics, Cryptography and Computing
(announcement and talk)Rochester, RIT Oct 7-9 2005. Vaclav Linek (talk) U. of Winnipeg, Winnipeg - 1 day January 2005 Banff Conference on Grid Computing Banff Conference Centre, Banff - summer 2005 Third Prairie Workshop U. of Winnipeg, Winnipeg - 2 days summer 2005 Southeastern International Conference on Combinatorics, Graph Theory and Computing March 2006 Carleton Math Days & Workshop on Coverings Carleton, Ottawa- summer 2006 Summer Meetings Canadian Math Society(invited half hour talk) Victoria - summer 2006 Fourth Prairie Workshop (invited 1 hour talk) U. of Lethbridge, Lethbridge - August 1, 2. 2006 R. Wei (talk) Lakehead U., Thunderbay - 5 days March, 2007 W. D. Wallis (talk) Southern Illinois U., Carbondale Ill. - 7 days April, 2007 Clement Lam Concordia University, Montreal - 3 days April 2007 Jeff Dinitz and Alan Ling (talk) U. of Vermont, Burlington - 5 days May 2007 Doug Stinson U. of Waterloo, Waterloo - 2 weeks June 2007
Professional Societies and Activities
University of Manitoba
Dalhousie University
University of Waterloo
The Stein_Lovasz Theorem and its Apllication to Some Combinatorial Arrays: D. Deng, Y. Zhang, P.C. Li and G.H.J. van Rees; J. of Combin. Math. & Combin. Computing, accepted Oct. 20, 2009.
More Greedy Defining Sets in Latin Squares: G.H.J. van Rees, Australasian Journal of Combinatorics, V44 (2009) 183-198. I thank the the Australasian Journal of Combinatorics for allowing me to use their copywrited version which can also be found at http://ajc.maths.uq.edu.au
On the spectrum of critical sets in latin squares of order 2^n: Diane Donovan, James LeFevre and G.H. John van Rees, J. of Combin., V 16 (2008) 25--43. See also Tech. Report.
When is a partial latin square uniquely completable, but not its completable product?: N. Cavenagh, D. Donovan, A. Khodkar and G.H.J. van Rees; Discrete Math. V308 (2008), 2830-2843.
There is no (22,8,4) Block Design:R.T. Bilous, C.W.H. Lam, L.H. Thiel, P.C. Li, G.H.J. van Rees,S.P. Radziszowski, W.H. Holzmann, H. Kharaghani; J. of Combinatorial Designs, V15 Issue 3, (2007) 262-267.
Nearly Orthogonal Latin Squares:P.C. Li & G.H.J. van Rees; J. Comb. Math. & Comb. Computing, V62 (2007) 13-24.
Constructions and Bounds for (m,t)-Splitting Systems-corrected and expanded version: D. Deng, D.R. Stinson, P.C. Li, G.H.J. van Rees, & R. Wei; Discrete Math., V307 (2007) 18-37.
Lotto Designs: P.C. Li & G.H.J. van Rees, section in "CRC The Handbook of Combinatorial Design", editors C. Colbourn & J. Dinitz, CRC Press Inc, (2007), 512-519
Constructions of 2-Cover_free Families and Related Separating Hash Families: P.C. Li, G.H.J. van Rees & R. Wei; J. of Combinatorial Designs, V14 (2006) 423-440.
Covering Designs on 13 Blocks Revisited: M. Greig, P.C. Li & G.H.J. van Rees; Utilitas Math. V70 (2006) 221-261.
Self-Dual Codes and the (22,8,4)Balanced Incomplete Block Design: R.T, Bilous & G.H.J. van Rees; J. of Combin Designs. V13 (2005) 363-376.
Several constructions of Non-Resolvable Steiner Triple Systems: P.C. Li & G.H.J. van Rees; Journal of Combinatorial Designs 13 (2005) 16-24.
Splitting Systems and Separating Systems: A.C.H. Ling, P.C. Li & G.H.J van Rees; Discrete Math, V279 (2004) 335-368.
Minimal and near-minimal critical sets in back-circulant Latin squares : J.A. Bate & G.H.J. van Rees; Australasian J. of Combin., V27 (2003) 46-62.
Lotto Design Tables: P.C. Li & G.H.J. van Rees; Journal of Combinatorial Designs, V10; (2002) 335-359.
An Enumeration of Binary Self-Dual Codes of Length 32: R.T, Bilous & G.H.J. van Rees; Designs, Codes and Cryptography, V26; (2002) 61-86. (See also Enumeration of the Binary Self-Dual Codes of Length 34: R.T. Bilous, J. of Combin. Math. Combin. Computing, V59 (2006) 173-211.)
A Note on Critical Sets J.A. Bate & G.H.J. van Rees, Australasian J. of Comb., V25; (2002) 299-302.
V(m,t) and its Variants,K. Chen, G.H.J. van Rees & L. Zhu, J. Stats. Plan. &Inf., V95 (2001) 143-160
New Constructions for Lotto Designs P.C. Li and G.H.J. van Rees, Utilitas Math. V58 (2000) 45-64.
V(m,t)'s for m=3,4,5,6, A.C.H. Ling, Y. LU, G.H.J. van Rees & L. Zhu, J. Stats. Plan. &Inf., V86 (2000) 515-525
An Application of Covering Designs: Determining the Maximum Consistent Set of Shares in a Threshold Scheme , R.S. Rees, D.R. Stinson, R. Wei & G.H.J. van Rees, Ars Comb. V53 (1999) 225-237
The size of the Smallest Strong Critical Set in a Latin Square, J.A. Bate & G.H.J. van Rees, Ars Combinatoria, V53 (1999) 73-83
Maximal Sets of Mutually Orthogonal Latin Squares,
D. Drake, G.H.J. van Rees & W.D. Wallis, Discrete Math.,
V194 (1999) 87-94 - also selected for
Special volume - Editor's Choice Discrete Math.
Lotto Designs J.A. Bate & G.H.J. van Rees, J. Comb. Math. & Comb. Computing, V28 (1998) 15-39.
Critical Sets in Back Circulant Rectangle, E. Mahmoodian & G.H.J. van Rees, Australasian Journal of Combinatorics, V16 (1997) 45-50.
Many (22,44,14,7,4) and (15,45,14,5,4) Balanced Incomplete Block Designs, D. Tiessen & G.H.J. van Rees, J. Stats & Inf., V16 (1997) 115-124
(r,lambda)-designs, G.H.J. van Rees, section in "CRC: The Handbook of Combinatorial Design", editors C. Colbourn & J. Dinitz, CRC Press Inc, (1996), 434-436. Also in "CRC: The Handbook of Combinatorial Design Second Edition", editors C. Colbourn & J. Dinitz, CRC Press Inc, (2006) 582-584.
(22,33,12,8,4)-BIBD, An Update, G.H.J. van Rees, a chapter in "Computational and Constructive Design Theory" ed. Wal Wallis, (1996) 337-357.
All v(3,t)'s Exist for 3t+1 a Prime, G.H.J. van Rees, Journal of Combinatorial Designs, V3 #6 (1995) 399-404.
Three Constructions of Covers, G.H.J. van Rees, Journal of Combinatorial Mathematics and Combinatorial Computing, V16, (1994), 19-25.
Some non-isomorphic (4t+4, 8t+6, 4t+3, 2t+2, 2t+1)-BIBDs, W.L. Kocay & G.H.J. van Rees, Discrete Math. , V92, (1991), 159-172.
Slightly Improved Upper Bounds for Equidistant Permutation Arrays of Index One, G.H.J. van Rees, Journal of Combinatorial Mathematics and Combinatorial Computing, V38, (1990), 159-160.
Some properties of finite bases for the Rosa set, R.C. Mullin, G. Gardner, K. Metsch & G.H.J. van Rees, Utilitas Math., V38, (1990), 199-215.
Subsquares and Transversals in Latin Squares, G.H.J. van Rees, Ars Combinatoria V29B (1990) 193-204.
Lottery Schemes and Covers, M. Morley & G.H.J van Rees, Utilitas Math., V37, (1990), 159-166.
A new family of BIBDs an non-embedabble (16,24,9,6,3)-designs, G.H.J. van Rees, Discrete Math., V77, (1989), 357-365.
Structures within (22,33,12,8,4)-Designs, J.A. Bate, M. Hall Jr. & G.H.J van Rees, Journal of Comb., Math, & Combin. Computing, V4, (1988), 183-194.
All non-isomorphic residual (16,24,9,6,3)-designs, G.H.J. van Rees, Journal of Combin. Math. & Combin. Computing, V3, (1988), 183-194.
On designs (22,33,12,8,4), M. Hall Jr., R. Roth, S.A. Vanstone & G.H.J. van Rees, J. of Combin. Math. A, V47, #2 (1988), 157-175.
Separable orthogonal Arrays, C.C. Lindner, R.C. Mullin & G.H.J. van Rees, Utilitas Math., V31, (1987), 25-32.
The equivalence of certain equidistant binary codes and symmetric BIBDs, D.R. Stinson & G.H.J. van Rees, Combinatorica, V4, (1984), 357-362.
Some Improved results concerning the Codes problem, D.R. Stinson & G.H.J. van Rees, Ars Combinatoria, V17, 1984), 117-128.
The solution of an iterated recurrence, D. Meek & G.H.J. van Rees, Fibonacci Quarterly, V22, #2, (1982), 263-281.
More Mutually orthogonal Latin squares, A.E. Brouwer & G.H.J. van Rees, Discrete Math., V39, (1982), 263-281.
Equidistant permutations arrays: A bound, S.A. Vanstone & G.H.J. van Rees, J. Austrailian Math. Soc., V33 (series A), (1982), 262-274.
Computation of some exact g-covers, R.G. Stanton, P. Eades, D. Cowan & G.H.J. van Rees, Utilitas Math., V18, (1980), 169-282.
On the construction of perpendicular arrays, R.C. Mullin, P.J. Schellenberg, S.A. Vanstone & G.H.J. van Rees, Utilitas Math, V18, 9180), 141-160.
Four pairwise orthogonal Latin squares of order 15, P.J. Schellenberg, S.A Vanstone & G.H.J. van Rees, Ars Combinatoria, V6, (1978), 141-150.
Some Constructions for equidistant permutation arrays of index one, K. Heindrich & G.H.J. van Rees, Utilitas Math., V13, (1978), 193-200.
Some results on a combinatorial problem of Cordes, D. McCarthy & G.H.J. van Rees, Austrialian Math. Soc., V23 (series A), (1978), 439-452.
On computing plethysms of Schurr-functions, P.A. Morris & G.H.J. van Rees, MATCH Informal Comm. in Math Chemistry, V3, (1977), 303-318.
The existence of balanced tournament designs, P.J. Schellenberg, S.A. Vanstone & G.H.J. van Rees, Ars Combinatoria, V3, (1977), 303-318.
The enumeration of generalized doubly stochastic non-negative integer square matrices, D.M. Jackson & G.H.J. van Rees, SIAM J. of Computing, V4 #4, (1975), 474-477.
On {123,124,134}-free Hypergraphs: P.C. Li, D.R. Stinson, G.H.J. van Rees & R. Wei, Congressus Numerantium, V183 (2006) 161-174.
A note on the completion of partial latin squares: N.J. Cavenagh, D. Donovan, & G.H.J. van Rees, Congressus Numerantium, V168 (2005) 109-118.
Finally C(19,6,2)=15, J.A. Bate, P.C. Li & G.H.J. van Rees, Congressus Numerantium, V157 (2002) 95-102.
Lower bounds on lotto designs, P.C. Li & G.H.J. van Rees, Congressus Numerantium, V141 (1999) 5-30.
A note on C(10,4,2) and C(11,5,3), G.H.J. van Rees, Congressus Numerantium, V99, (1994), 271-275.
Single Change Designs II, G.H.J. van Rees, Congressus Numerantium, V92, (1993), 29-32.
On the maximum number of implants needed to cover a multiple-valued logic function using window literals, G.W. Dueck & G.H.J. van Rees, Proceedings of 21st International Symposium on Multiple-Valued Logic (IEEE), Victoria, B.C. (1991) 1-13.
An idealization of number theory problem in combinatorial design theory, G.H.J. van Rees, Congressus Numerantium, V57, (1987), 213-222.
Some results on N(4,6,10), N(4,6,11) and related coverings, J.A. Bate & G.H.J. van Rees, Congressus Numerantium, V48, (1985), 25-45.
Some large critical sets, D.R. Stinson & G.H.J. van Rees, Congressus Numerantium, V31, (1981), 267-273.
On Latin Queen squares, G.H.J. van Rees, Congressus Numerantium, V31, (1981), 267-273.
A general construction for equidistant permutation arrays, K. Heinrich, W.D. Wallis & G.H.J. van Rees, Proceedings of Graph Theory and Related Topics, a conference in honour of W.T. Tutte, (1979), 247-252.
Critical sets in Latin Squares, D. Curran & G.H.J. van Rees, Congressus Numerantium, V22, (1978), 165-168.
The non-existence of (7,1)-designs with v=31, b=48 or 49, G.H.J. van Rees, Congressus Numerantium, V18, (1976), 469-494.
Pedagogical Ariticles (refereed)
Knight's Tours and Circuits, G.H.J. van Rees, Bulletin of ICA, V16 (1996) 81-86.
The spectrum of critical sets in latin squares of order 2^n: Diane Donovan, James LeFevre and G.H. John van Rees
Lovasz Local Lemma,: G.H.J. van Rees
Frequency and Lotto Designs P.C. Li & G.H.J. van Rees
Transversals in Rectangles: G.H.J. van Rees
Lotto Designs
TransTalk
Banfftalk
Vermonttalk
Montrealtalk
website for self-dual
binary codes of length up to 34
web site for
lotto tables
Download John Bate's program for finding
Critical Sets
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