Name: William Edwin Clark
Initial Date of USF Employment/Rank: September, 1970/Professor
Present Rank (effective date): Professor Emeritus (May, 2003)
Tenured (effective date): September, 1972
Sam Houston State University, Mathematics, B.S., 1960
Tulane University, Mathematics, Ph.D., 1964
Professor Emeritus, University of South
Professor, University of South Florida, 1970-2003
Associate Professor, University of Florida, 1968-1970
Assistant Professor, University of Florida, 1965-1968
Postdoctoral Fellow, CalTech, 1964-1965
Military Service, U. S. Army (Japanese Interpreter), 9/53-6/57
Woodrow Wilson Fellowship (1960-1961)
Ford Foundation Postdoctoral Fellowship (CalTech 1964-1965)
Teaching Award (TIP) from USF 1996
American Mathematical Society
Mathematical Association of America
Institute for Combinatorics and Its Applications
Research Publications: (All Refereed Journals)
1. Affine Semigroups over an arbitrary field, Proc. Glasgow Math. Assoc., 7 (1965), pp. 80-92.
2. Remarks on the kernel of a matrix semigroup, Czezh. Math. J. 15 (90), (1965), pp. 305-309.
3. Weakly semi-simple finite dimensional algebras, Can. J. Math., Vol. 18, (1966), pp. 433-442.
4. Baer rings which arise from certain transitive graphs, Duke Math. J., Vol. 30, No. 4, (1966), pp. 647-656
5. Twisted matrix units semigroup algebras, Duke Math. J., Vol. 34, No. 3 (1967), pp. 418-424.
6. Algebras of global dimension one with a finite ideal lattice, Pacific J., Vol. 23, No. 3 (1967), pp. 463-471.
7. A note on semiprimary PP-rings, Osaka J. Math., 4, (1967), pp. 177-178.
8. On minimal ideals in the circle composition semigroup on a ring (with Jacques Lewin), Pub. Math. (Debrecen), Tomus 14, (1967), pp. 99-104.
9. Generalized radical rings, Can. J. Math., Vol. 20, (1968), pp. 88-94
10. Murase's quasi-matrix rings and generalizations, Sci. Papers of College of Gen. Ed., University of Tokyo, Vol. 18, (1968), pp. 99-109.
11. On the categoricity of semigroup theoretical properties, (with Burrow P. Brooks), Semigroup Forum, Vol. 3, ( 1971), pp. 259-266.
12. On the coeficient ring of a finite non-commutative ring, Proc. Amer. Math. Soc., Vol. 33, No. 1. May, 1972, pp. 25-28.
13. The automorphism class group of the category of rings, (with G. M. Bergman, J. of Algebra, Vol. 24, January, 1973, pp. 80-99.
14. Finite chain rings, (with David A. Drake), Abh. Math. Sem. Hamburg, Band 39, September, 1973, pp. 147-153.
15. Enumeration of finite commutative chain rings, (with J.J. Liang), Journal of Algebra, Vol. 27, December, 1973, pp. 445-453.
16. On arithmetic weight for a general radix representation of integers, (with J.J. Liang), IEEE Transactions on Information Theory, Vol. 19, November, 1973, pp. 823-826.
17. On modular weight and cyclic nonadjacent forms for arithmetic codes (with J. J. Liang), IEEE Transactions on Information Theory, Vol. IT-20, Nov. 1974, 767-770.
18. Is topologically simple simple? (with Mukherjea and Tserpes) Semigroup Forum., Vol. 11 No. 1-1975, pp. 90-94.
19. Weak radix representation and cyclic codes over Euclidean rings, (with J.J. Liang), Communications in Algebra, 4 (11), 1976, 999-1028.
20. Cohomology of semigroups via topology-with an application to semigroup algebras, Communications in Algebra, 4 (10), 1976, 979-997.
21. Equidistant cyclic codes over GF(q), Discrete Math. 17, (1977), 139-141.
22. Rings Euclidean for a valuation and radix representation over Euclidean rings, (with J.J. Liang), Proc. Nat. Sci. Council (Taiwan), Vol. 3, No. 4, 335-337, (1980).
23. Comments on a functional equation (with Mukherjea), Real Analysis Exchange, Vol. 6, No. 2, (1980-81), 192-199.
24. Equidistant binary arithmetic codes, (with J.J. Liang), IEEE Transactions on Information Theory, IT-32, No.1, Jan.,1986, pp. 106-108.
25. Cyclic codes over GF(q) with simple orbit structure, Discrete Mathematics, 60 (1986), pp. 1-14.
26. Remarks on the Sharma-Kaushik metrics for error-control codes (with Gur Dial), Journal of Combinatorics, Information & System Sciences, vol 13, Nos 3-4, 1988, pp. 74-78.
27. The construction of some bit and byte error control codes using partial Steiner systems ( with L. Dunning and D. Rogers). IEEE Transactions on Information Theory, IT-36, Nov. 1989, pp. 1305-1310.
28. Prime cyclic arithmetic codes and the distribution of power residues (with L. Lewis). Journal of Number Theory, June 1989, pp. 220-225.
29. Binary set functions and parity check matrices (with L. Dunning and D. Rogers), Discrete Mathematics, 80, 1990, pp. 249-265.
30. Blocking sets in finite projective spaces and uneven binary codes, Discrete Mathematics 94, 1991, pp. 65-68.
31. Partial partitions of vector spaces arising from the construction of byte error control codes (with L. Dunning), Ars Combinatoria 33, 1992, pp. 161-177.
32. On the complexity of deadlock free programs on a ring of processors (with W. R. Stark and G. L. McColm), Journal of Parallel and Distributed Computing 16, 1992, pp. 67-71.
33. Bounds on a class of partial partitions of a vector space over GF(2): A graph theoretical approach, Linear and Multilinear Algebra 32, 1992, pp. 225-235.
34. Matching subspaces to complements in finite vector spaces, Bulletin of the Institute of Combinatorics and its Applications, 6, 1992, pp. 33-38.
35. Sum-free sets in vector spaces over GF(2). (with John Pedersen), Journal of Combinatorics (Series A) 61, 1992, pp. 222-229
36. The domination numbers of the 5xn and 6xn grid graphs, (with T. Chang), Journalof Graph Theory, Vol. 17, No. 1, pp. 81-107, 1993
37. Domination numbers of complete grid graphs, I (with T. Chang and E. O. Hare), Ars Combinatoria 38, 1994, pp. 97-111
38. q-Analogue of a binomial coefficient congruence, International Journal of Mathematics and Mathematical Science, Vol. 18, No. 1, 1995, pp. 197-200
39. Separating sets with parallel classes of hyperplanes, Bulletin of the Institute of Combinatorics and its Applications, Vol. 13, 1995, pp. 65-82
40. Covering by Complements of Subspaces, Linear and Multilinear Algebra,(with Boris Shekhtman), Vol 40, 1995, pp. 1-13.
41. Domination numbers of q-analogues of Kneser graphs (with Boris Shekhtman), Bulletin of the Institute of Combinatorics and its Applications, Vol. 13, 1995, pp. 65-82
42. On the domination matrices of the C-analogues of Kneser graphs (with Boris Shekhtman), Congressus Numerantium 107 (1995), 193--197.
43. Binomial and q-binomial coefficient inequalities related to the hamiltonicity of the Kneser graphs and their q-analogues, (with M. Ismail), Journal of Combinatorial Theory (Ser. A.) , Vol. 76, No;l 1, Oct. 1996, pp. 83-98.
44. Tight Upperbounds for the Domination Number of Graphs of Given Order and Minimum Degree. (with Larry Dunning). Electronic Journal of Combinatorics 4 (1997), no. 1, Research Paper 26, 1-25.
45. Covering by Complements of Subspaces, II (with Boris Shekhtman), Proc. Amer. Math. Soc. 125 (1997), no. 1, 251-254.
46 Domination Numbers of q-Analogues of Kneser Graphs (with B. Shekhtman), Bulletin of the Institute of Combinatorics and its Applications. 19 (1997), 83-92.
47. On the Domination Number of Certain Analogues of Kneser Graphs (with B. Shekhtman), Congressus Numerantium. 126 (1997), 175-181.
48. k-Point Separating Families of Functions (with Gregory McColm and Boris Shekhtman), J. of London Math. Soc.(1998), no. 2, 297-310.
49. Decompositions in discrete semigroups, (with W. C. Holland and G. J. Székely, Studia Sci. Math. Hungar. 34 (1998), no. 1-3, 15--23.
50. Upper bounds for the domination number of a graph., (with B. Shekhtman, S. Suen,and D. C. Fisher), Congressus Numerantium 132 (1998), 99--123.
51. On the probability that a t-subset of a finite vector space contains an r-subspace - with applications to short, light codewords in a BCH code, (with Stephen Suen), Congressus Numerantium 137 (1999), 139-159.
52. An Inequality Related to Vizing's Conjecture, with Stephen Suen, Electronic Journal of Combinatorics, Volume 7 (1), (2000) N4.
53. Tight Upper Bounds for the Domination Numbers of Graphs with Given Order and Minimum Degree, II, with Larry Dunning and Stephen Suen, Electronic Journal of Combinatorics,Ý Volume 7 (1), 2000, R58
54. Inequalities Involving Gamma and Psi Functions, with Mourad Ismail, Analysis and Applications, Volume 1, Number 1, January 2003, 129--140.
55. Application of Upper
and Lower Bounds for the DominationNumber to Vizing's Conjecture ,
(with Mourad Ismail and StephenSuen), Ars
69 (2003), 97-108.
More Recent Publications
Grants and Contracts
NSF research grant (GP-7623) entitled: "Algebras of finite global dimension" (1967-69)
USF release time grant (1973)
NSF research grant (ENG 77-00436) entitled: "Algebraic coding over Euclidean domains" with J.J. Liang (1977-1978)
Department of Defense (National Security Agency), Special Assignment, 8-96-9-97.
Doctoral Dissertations Directed:
C. K. Martin, Distinguished rings of linear
University of Florida, 1966.
J. M. Kellet, A torsion theory
University of Florida,1968.
W. T. Spears, On categories of diagrams,
University of Florida, 1968.
B. P. Brooks, Jr., Co-rings in the category of
University of Florida,1970.
S. J. Maxwell, Certain well-factored categories,
University of Florida, 1970.
T. Y. Chang, Domination numbers of grid graphs,
University of South Florida, 1992.
M, Pseudo-orthogonal complementary subspaces and
hyperbolic partner subgraphs,
University of South Florida, 1996.
Masters Thesis Directed:
K. L. Moss, The category of rings,
University of Florida, 1969.
Jean M. Dickson, Perfect Dominating Sets in Graphs
University of South Florida, 1993
List of Courses and Seminars Taught at USF
Abstract Algebra for Teachers
Abstract Algebra I and II
Advanced Calculus I and II
Algebraic Automata Theory
Algebraic Coding Theory
Applied Matrix Theory
Calculus (Elementary, Engineering and Regular)
Combinatorics I and II
Elementary Abstract Algebra
Elementary Linear Algebra
Elementary Number Theory
Majors and Honors Seminars
Symbolic Computations in Mathematics
Applications of Linear Algebra to Combinatorics
Applied Number Theory
Clifford and Grassman Algebras
Combinatorics of Finite Sets
Finite Metric Spaces
Introduction to Combinatorics
Introduction to Maple
Linear Algebra Over Finite Fields
Tensor Analysis on Manifolds
Algebraic Coding Theory
Uniform Subset Graphs and Their q-Analogs