L.J. CUMMINGS Ph.D. 1967 Mathematics University of British Columbia Dissertation: Linear Transformations of Symmetric Tensor Spaces which Preserve Rank 1. Employment Record 1993 Visiting Professor School of Computing, Perth 1988 Visiting Professor University of Paris VII, LITP 1988 Visiting Professor University College, Dublin 1984-P Professor University of Waterloo 1986 Visiting Professor Southern Illinois University, U.S.A. 1981 Visiting Professor University of Oslo, Norway 1981 Visiting Scientist Utah State University, U.S.A. 1975 Visiting Professor University of Newcastle, Australia 1974-84 Associate Professor University of Waterloo 1974-75 Visiting Lecturer University of St. Andrews, Scotland 1967-76 Assistant Professor University of Waterloo Area of Interest: Multilinear Algebra, Combinatorics on Words PUBLICATIONS In refereed journals 1. L.J. Cummings, Gray paths of Lyndon words in the N-cube, Congressus Numerantium 69 (1989), 199-206. 2. L.J. Cummings and J. Yukas, Paths of Lyndon words. The Journal of Combinatorial Mathematics and Combinatorial Computing 6 (1989), 63-66. 3. L.J. Cummings, Connectivity of synchronizable codes in the n-cube, J. of Combinatorial Mathematics and Combinatorial Computing, 3 (1988), 93-96. 4. L.J. Cummings, Aspects of Synchronizable Coding, JCMCC 1 (1987), 67-84. 5. L.J. Cummings and D.H. Wiedemann, Embedded deBruijn Sequences, Congressus Numeratium 53 (1986), pp. 155-160. 6. L.B. Beasley and L.J. Cummings; Test sets for generalized matrix functions, Linear and Multilinear Algebra 17 (1985), 301-307. 7. L.J. Cummings; Synchronizable Codes in the De Bruijn graph, Ars Combinatoria 19 (1985), 73-80. 8. L.J. Cummings; Matrix problems in synchronizable coding, Linear Algebra and its Applications, 59 (1984), 186-188. 9. L.J. Cummings; Comma-free codes in the De Bruijn graph, Caribbean Journal of Mathematics 2 (1984), 65-68. 10. L.B.Beasley and L.J. Cummings; On the uniqueness of generalized matrix functions, Proc. Amer. Math. Soc. 87 (1983), 229-232. 11. L.J. Cummings and B.C. de Gopi; Maximal incidence algebras, Ars Combinatoria, 13 (1982), 145-147. 12. L.B. Beasley and L. Cummings; Multiplicative properties of generalized matrix functions, Linear and Mutlilinear Algebra 11 (1982), 23-31. 13. L.B. Beasley and L. Cummings; Permanent semigroups, Linear and Multilinear Algebra 5 (1978), 297-302. 14. L.J. Cummings; Maximum comma-free codes as cosets of linear codes, Ars Combinatoria, 3 (1977), 115-122. 15. L.J. Cummings and J.S. Wallis; An algorithm for the permanent of circulant matrices, Canadian Math. Bull., 20 (1977), 67-70. 16. L.J. Cummings and R.W. Robinson; Linear symmetry classes, Canadian J. Math. 28 (1976), 1311-1319. 17. A. Ball and L. Cummings; Extremal digraphs and comma-free codes, Ars Combinatoria 1 (1976), 239-251. 18. A. Ball and L. Cummings; The comma-free codes with words of length two, Bull. Australian Math. Soc. 14 (1976), 249-258. 19. L.J. Cummings; Cyclic symmetry classes, Journal of Algebra, 40 (1976), 401-405. 20. L.J. Cummings and D.A. Fox; Some mathematical properties of cycling strategies citation indexes, Inform. Stor. Retr. 9 (1973), 713-719. 21. L.B. Beasley and L. Cummings; Permanent groups II, Proc. Amer. Math. Soc. 40 (1973), 358-364. 22. L.J. Cummings; Transformations of symmetric tensors, Pacific J. Math. 42 (1972), 603-613. 23. L.B. Beasley and L. Cummings; Permanent groups, Proc. Amer. Math. Soc. 34 (1972), 351-355. 24. J.L. Brenner, L. Cummings; The Hadamard maximum determinant problem, Amer, Math. Monthly 79 (1972), 626-630. 25. L.J. Cummings; Decomposable symmetric tensors, Pacific J. Math. 35 (1970), 65-77. 26. L.J. Cummings; Characteristic roots of rank 1 matrices, Amer. Math. Monthly 77 (1968), 1105-1106. Papers accepted in refereed journals 27. "Shuffled Lyndon Words'' (with M.E. Mays), accepted by W. Kocay for Ars Combinatoria, February 14, 1990. 28. "Gray Arrays and Gray Tori", accepted by A. Odlyzko for Journal Combinatorial Theory, February 9, 1990. 29. "Schur Extensions" (with L.B. Beasley), accepted by R. Brualdi for Lineart Algebra and its Applications, November 8, 1990. 30. "Semigroups of Matrices over Semirings" (with L.B. Beasley), accepted by R. Rees for the "Festschrift in honour of N. Pullman", October 29, 1990. 31. "Gray Codes and Strongly Square-Free Strings" accepted by R. Capocelli, for Sequences 1991, Springer-Verlag September 5, 1991. Research & Scholarship - 4 - L.J. Cummings Papers in refeered conference proceedings L.J. Cummings, "Sequences of Lyndon Words", in Sequences, Springer-Verlag, 1990, 156-165. L.J. Cummings, A Hamilton Path Construction for Lyndon Words in the N-cube, Proceedings of the 5th Carribbean Conference in Combinatorics and Computing. University of the West Indies, Cave Hill, (1988), 33-40. L.J. Cummings; Strongly qth power-free strings, Proceedings for the Colloque International sur la Theorie des Graphes et Combinatore. North Holland, (1983), 247-252. L.J. Cummings; Overlapping Substrings and Thue's Problem, Proceedings of the Third Caribbean Conference in Combinatorics and Computing, University of the West Indies, Barbados, (1981), 99-109. L.J. Cummings; On the construction of Thue sequences, Proceedings of the Ninth Southeastern Conference on Combinatorics, Graph Theory and Computing, Florida Atlantic University, Boca Raton, (1978), 235-242. A. H. Ball and L. Cummings; Lower for CF (n,6) codes, Proceedings of the Seventh Manitoba Conference on Numerical Mathematics, University of Manitoba, Winnipeg, (1977), 177-190. L.J. Cummings and W.D. Wallis; A transversal algorithm for regular square incidence matrices, Eight Southeastern Conference on Combinatorics, Graph Theory and Computing, March 1977, Louisiana State University, 213-226. L. Cummings; Are maximum synchronizable codes linear? Proceedings of the Second Caribbean Conference in Combinatorics and Computing, University of the West Indies, Barbados, (1977), 107-114. L. Cummings; Comma-free codes and incidence algebras (invited address), Proceedings of the fourth Australian Conference on Combinatorical Mathematics, Adelaide 1975, Lecture Notes in Mathematics, Vol. 560, Springer-Verlag, Berlin (1976), 1-6. Paper in unrefereed journal L. Cummings; Dimers, Ontario Secondary School Math. Bull. 14 (1978), 21-25. Paper in unrefereed conference proceedings L. Cummings; Elementary-maximal permanent semigroups, Fourth Southeastern Conference on Combinatorics, Graph Theory and Computing, March 1973, Florida Atlantic University, Boca Raton, (1973), 233-236. Book L.J. Cummings, Ed., "Combinatorics on Words, Progress and Perspectives", Academic Press, Inc. New York, 1983. Invited addresses at conferences 1991, June 20: "Gray Codes and Strongly Square-Free Strings", Sequences 91, Positano, Italy. 1991, April 19: "Strongly Square-Free Stings and Uniform Morphisms", Combinatorial Pattern Matching, Royal Holloway and Bedford New College, Surrey. 1988 March 11: "A Characterization of the Permanent Function by the Binet-Cauchy Theorem", Dublin Matrix Theory Conference, Dublin, Ireland. 1986 April 10: "The Construction of Comma-Free Codes", Carbondale Combinatorics Conference, Southern Illinois University. 1986, April 11: "Synchronizable Coding in the de Bruijn Graph", Carbondale Combinatorics Conference, Southern Illinios University. 1985, October 4: "Factorizations and Synchronizable Coding", Combinatorial Algorithms in Algebraic Structures Conference, Universitat Kaiserslautern, West Germany. 1984, June 2-4: Invited participant Combinatorial Matrix Theory Workshop, Queen's University. 1983, June: "Matrix Problems in synchronizable coding", Third Matrix Theory and Applications Conference, Utah State University. 1975, August 28: "Comma-free Codes and Incidence Algerbras", Fourth Australian Conference on Combinatorial Mathematics, University of Adelaide, South Australia. Invited Hour Addresses 1988, September 6: "Synchronizable Codes", Colloquium, West Virginia University, Morgantown. 1988, June 11: "Sequences of Lyndon Words", Workshop on Sequences, Combinatorics, Compression, Security, and Transmission, Positano, Italy. 1988, June 11: "Sequences of Lyndon Words", Workshop on Sequences, Combinatorics, Compression, Security, and Transmission, Positano, Italy. 1988, June 2: "Non-Counting Congruences of Order 2", Colloquim, University of Paris North, St. Denis. 1988, May 16: "Non-Counting Congruences of Order 2", Seminaire des Languages. University of Paris. 1988, February 11: "New Results on Hadamard Matrices II,""Seminar, Southern Illinois University. 1988, February 4: "New Results on Hadamard Matrices I", Seminar, Southern Illinois Univerisity 1988, January 28: "A Hamilton Path Construction for Lyndon Words in the N-cube", Colloquium, Southern Illinois University. 1988, January 28: "A new Proof of the Golomb-Gordon theorem", Seminar, Southern Illinois University. 1988, January 15: "Synchronizable codes in the N-cube", Colloquium, Auburn University, 1986, April 2: "The Construction of Thue Sequences", Southern Illinois University, Mathematics Department Colloquium. 1986, April 2: "Synchronizable Coding", Southern Illinois University, Combinatorics Seminar. 1986, March 26: "On Comma-Free Codes", Southern Illinois University, Combinatorics Seminar. 1984, March 13: "On Generalized Matrix Functions", Utah State University. 1984, February 2: "On Thue Sequences", Utah State University Colloquium. 1983, March 24: "Gerenalized Matrix functions", University of Toronto, Algebra Seminar. 1982, April 27: "Construction of Comma-Free Codes, SIAM Conference on Applied Linear Algebra, Raleigh, North Carolina. 1982, February 9: "Comma-Free codes in the de Bruijn graph", Coxeter seminar, University of Toronto, Toronto. 1981, November 17: "The Contruction of Comma-Free Codes", Utah State University, Logan, Utah. 1981, June 11: "On Construction of Thue Strings", Mathematical Institute, Oxford, U.K. . 1981, March 3: "The work of Axel Thue", University of Oslo. 1981, February 26: "On the Construction of Thue-Sequences", The Mittag-Leffler Institute, Stockholm, Sweden, (2 Hours!). 1981, February 24: "On Thue-Sequences", University of Stockholm, Sweden, (2 Hours!). 1980, November 12: "The Morse-Hedlund Sequence", University of Waterloo Number Theory Seminar. 1975, November 4: "Permanent Difficulties", University of Queensland, Colloquium, Brisbane, Australia. 1975, October 3: "Permanent Difficulties", University of Newcastle, Seminar, New South Wales, Australia. 1973, October 18: "Symmetry Classes of Tensors", Pure Mathematics, Colloquium, University of St. Andrews, Scotland. Talks Presented 1990, September 28: "On the Parity of the Witt Formula", 20th Manitoba Conference, University of Manitoba. 1990, November 2: "Gray Codes and Square-Free Sequences", Fifth Carbondale Conference, Southern Illinois University.s 1989, February 22: "Circular Hammings Arrays", The S.E. Conference on Combinatorics, Graph Theory Computing, Florida Atlantic University. 1989, May 26: "Arrays of Lyndon words", The Washington Conference on Combinatorics and theoretical Computer Science, George Washington University. 1989, November 18: "Paths of Lyndon words", (with J. Yukas), University of Manitoba. 1988, October 22: "Arrays of Lyndon Words," 3rd Carbondale Combinatorics Conference, Southern Illinois University, Carbondale. 1988, December 13: "Sequences of Lyndon Words in the N-cube", Canadian Mathematical Society Winter meeting. 1986, February 21: "Embedded de Bruijn Sequences", Seventeenth Southeastern International Conference on Combinatorics, Graph Theory and Computing, Florida Atlantic University. 1985, March 30: "Test Sets for Generalized Matrix Functions", 73rd Ontario Mathematical Meeting, Brock University, St. Catharines. 1985, March 23: Ontario Combinatorics Workshop. 1985, February 2: Colloquium, Utah State University. 1984, March 6: "Sychronizable codes in the De Bruijn graph", Fifteenth Southeastern Conference on Combinatorics, Graph Theory and Computing, Florida Atlantic University. 1984, January 26: "The structure of generalized permanent semigroups, 90th Annual Meeting of the American Mathematical Society, Louisville, Kentucky. 1983, March 26: "Generalized Matrix Functions", Ontario Math Meeting, Queen's University. 1982, February 15: "Inequality defined comma-free codes", Thirteenth Southeastern Conference on Combinatorics, Graph Theory and Computing, Florida Atlantic University. 1981, July 22: "On the construction of Thue sequences", Eighth British Combinatorial Conference, University College, Swansea. 1981, July 6: "Comma-free codes in the de Bruijn graph" Sixth Hungarian Colloquium on Combinatorics, Eger, Hungary. 1981, June 15: "Strongly qth-power free strings", Colloque International du centre National de la Recherche Scientifique, University of Marseille-Luminy. 1981, January 8: "On the Construction of Thue sequences II, "Third Caribbean Conference on Combinatorics and Computing, the University of West Indies, Cave Hill, Barbados. 1978, March 18: "On the construction of Thue sequences", IX Colloque Des Mathematiciens Du Quebec and 47th Ontario Mathematics Meeting, Ottawa. 1978, February 1: "On the construction of Thue sequences", Ninth Southeatern Conference on Combinatorics, Graph Theory and Computing, Florida Atlantic University, Boca Raton. 1977, October 15: "Products of comma-free codes", 44th Ontario Mathematical Meeting, Brock University, St. Catharines. 1977, July: "Products of comma-free codes", Sixth British Combinatorial Conference, Royal Holloway College, University of London. 1977, March 26: "Linear Symmetry Classes", 43rd Ontario Mathematical Meeting, Carleton University. 1977, January 27: "Permanent semigroups" 83rd Annual meeting of the American Mathematical Society, St. Louis. 1977, January 6: "Are synchronizable codes linear?", Second Caribbean Conference on Combinatorics and Computing, University of the West Indies, Barbados. 1976, June 3: "Comma-free codes", Canadian Mathematical Congress Summer Meeting, University of New Brunswick. 1976, February 11: "Digraphs containing no paths of length 3", Seventh Southeastern Conference on Combinatorics, Graph Theory and Computing, Baton Rouge. 1975, May 22: "Symmetry classes" Tenth New Zealand Mathematical Colloquium, University of Otago, Dunedin. 1975, May 13: "Cyclic symmetry classes" Annual Australian Mathematical Society meeting, James Cook University, Townsville, Queensland. 1973, June 9: "Computation of the permanent and the dimer problem", Canadian Mathematical Congress, Twenty-Seventh Summer Meeting, Trent University. 1973, March 8: "Elementary-maximal permanent semigroups", Fourth Southeastern Conference on Combinatorics, Graph Theory and Computing, Florida Atlantic University, Boca Raton. 1973, January 28: "Nonsingular matrix groups for which the permanent function if multiplicative", Seventh-Ninth Annual Meeting of the American Mathematical Society, Dallas. 1972, October 28: "Permanent groups", Twenth-Fourth Ontario Mathematical Meeting, University of Western Ontario. Recent Waterloo Seminars 1990, February 1: "On the Parity of the Witt Function", Algebra Seminar. 1989, October 13: "Error-correcting Codes, II", Information Theory Seminar. 1989, October 11: "Error-Correcting Codes, I", Information Theory Seminar 1986, January 20: "Lyndon Words", Algebra Seminar. 1985, March 26: "Test sets for matrix functions", Algebra Seminar. 1984, September 26: "An Introduction to Error-correcting Codes, II", Information Theory Seminar. 1984, September 24: "An Introduction to Error-Correcting Codes, I", Information Theory Seminar. 1984, February 15: "Mutliplicative Properties of Schur Functions", Algebra Seminar. 1983, March 27: "Commutators and the Lower Central Series I", Group Theory Seminar. 1983, March 21: "Commutators and the Lower Central Series II", Group Theory Seminar. 1983, January 26: "Generalized Matrix Functions", Algebra Seminar. 1982, November 4: "Avoidable Patterns in Strings", Number Theory Seminar. 1980, November 17: "Dimensions of Linear Symmetry Classes", Enumeration Seminar. 1980, October 5: "Thue Sequences", Number Theory Seminar. 1979, February 23/26: "Synchronizable Codes and Comma-free Codes", Information Theory Seminar. 1978, February 28: "Comma-free Codes and Incidence Algebras", Algebra Seminar. Invited participant: Combinatorial Matrix Theory Workshop, Queen's University, June 2-8, 1984. GRADUATE STUDENT SUPERVISION M. Math G.T. Glashan (graduated October 1970) A. Bakos (graduated May 1973) H. Kommel (started Sept. 79 - graduated Oct. 82) M.Phil J. MacDougall (graduated May 1979) Title: Rank Problems in Grassmann Products Ph.D. J. Wu (graduated May 1995) Title: Constructing Algebras of Symmetry Classes of Tensors R. Craigen (graduated May 1991) Title: Constructions for Orthogonal Matrices A. Ball (Comb. & Opt.) (graduated May 1980) Title: The Construction of Comma-free Codes with Odd Word Length R. Craigen (Sept.1987-present) H. Kommel (graduated October 1985) Title: On the Noncounting Congruence of Order 2. D. Wiedemann (Jan. '86 - Dec. '86) (Joint with R. Mullin, C&O) Title: Hamming Geometry L. Zhang (Sept. 1988-Dec.1989 - transferred supervision) Summer NSERC Undergraduate Student K. Jardine (1985) - joint supervision with F.C.Y. Tang, K. Geddes University Committees University Senate (1991-93) Long Range Planning Committee (1992-93) Pension and Benefits Committee (1978-79) Library Fines Appeal Board (1978-79) Executive Committee, Faculty Association (1978-79) Academic Freedom and Tenure (1978-79) Grievance Procedures Committee (1983-85) Faculty Committees Graduate Committee (1982-87) Undergraduate Admissions Committee (1984-86) Department Committees Graduate committee (1994-96) Executive Committee: 1977-79 1983-87 1988-89 Promotion Committee: 1978-79 Tenure Committee: 1969-present Chairmanship Selection Committee: 1978 Curriculum Committee: 1988-90 Professional Activities Societies Canadian Mathematical Society American Mathematical Society Mathematical Association of America Australian Combinatorial Society London Mathematical Society Refereeed For Pacific Journal of Mathematics Journal of the Australian Mathematical Society Malaysian Journal of Science Ars Combinatoria Linear Algebra and its Applications Journal of Combinatorial Theory Aequationes Mathematicae American Mathematical Monthly Canadian Journal of Mathematics Information and Control Reviewing Activities Reviews of both Linear Algebra and Multilinear Algebra by W. H. Greub, Canada. Math. Bull. 11 (1968), 512-513. Review of "Abstract Algebra - A Computational Approach" by C.C. Sims in APL Quote Vol. 16, No. 3 (March, 1986) Editorial Duties Collaborating Editor, American Mathematical Monthly, Problems section, 1978-81. Editor, Combinatorics on Words, Progress and Perspectives, Academic Press, 1984. Editor, Combinatorial Mathematics and Combinatorial Computing, 1989-present. Other Organizer, Mathematics Club, K-W Bilingual School (1979-81) Orgainzer, First International "Combinatorics on Words" Conference, 1982. Organizer, Multilinear Algebra week, July 17-21, 1983. Organizer, Algebra Seminar, Pure Mathematics (1983-84) Organizer, Pure Mathematics Cayley Group (1984-87). Organizer, Algebra Seminar, Pure Mathematics (1986-87)