Research Papers

With the help of Chris Tuthill of Fogler Library, I am getting my papers onto this website. All the entries that have hyperlinks on the titles will permit you to download a pdf of the paper. My goal is to eventually put all my papers on my web site. In the meantime, If you would like a copy of one of them that is not up yet, please send e-mail to:
  1. Cardinalities of D-Classes in Bn Semigroup Forum 4, 1972, 341-344 (with Brandon, Butler, Hardy).
  2. The Schutzenberger Group of an H-Class in the Semigroup of Binary Relations Semigroup Forum 5, 1972, 45-53 (with Brandon, Hardy).
  3. Indempotents and Product Representations with Applications to the Semigroup of Binary Relations Semigroup Forum 5, 1972, 95-119.
  4. The Number of Maximal Subgroups of the Semigroup of Binary Relations Kyungpook Math J., 12, June 1972, 1-8 (with Butler).
  5. The Number of Maximal Subgroups of the Semigroup of Binary Relations II Kyungpook Math J., 12, December 1972, 199-211 (with Butler).
  6. Enumeration of Finite Topologies Proc. 4th S. E. Conference on Combinatorics, Graph Theory and Computing, Boca Raton, 1973, 169-184 (with Butler).
  7. Some Combinatorial Aspects of Lattice Theory Proc. Univ. of Houston Lattice Theory Conf., 1973, 36-68.
  8. The Number of Partially Ordered Sets II J. Korean Math. Soc., 11, April 1974, 7-17 (with Butler).
  9. The Factorization and Representation of Lattices Trans. Am. Math. Soc. 203, 1975, 185-200.
  10. On Dedekind's Problem: The Number of Isotone Boole an Functions II Trans. Am. Math. Soc. 213, 1975, 373-390 (with Kleitman).
  11. Chain-complete Posets and Directed Sets with Applications Algebra Univ.6, 1976, 53-68.
  12. Bases for Chain-complete Posets IBM J. R&D, 20, 1976, 138-147 (with Rosen).
  13. Lower Bounds on the Length of Node Sequences in Directed Graphs Discrete Math. 16, 1976, 329-337 (with Tarjan).
  14. Categories of Chain-Complete Posets Theoretical Computer Science 4, 1977, 125-135.
  15. Bounds on the Index and Period of a Binary Relation on a Finite Set Semigroup Forum 13, 1977, 253-259.
  16. Subprojective Lattices and Projective Geometry J. Algebra 48, 1977, 305-320 (with Petrich).
  17. Multidimensional Bin Packing Algorithms IBM J. R&D, 21, 1977, 443-448 (with Kou).
  18. Exact and Approximate Membership Testers In Proc. 10th Ann. Symp. on Theory of Computing(SIGACT),May 1978, 59-65 (with Carter, Floyd, Gill, Wegman).
  19. A Mathematical Analysis of Human Leukocyte Antigen Serology Math. Biosciences 40, 1978, 243-270 (with Nau, Woodbury, Amos).
  20. Differential Operators and the Theory of Binomial Enumeration J. Math. Analysis and Applications, 63, 1978, 145-155.
  21. On The Number of Prime Implicants Discrete Math. 24, 1978, 7-11 (with Chandra).
  22. Analysis of a Universal Class of Hash Functions Proc. 7th Symposium on the Math. Foundations of Computer Science in Zakopane, Poland, 1978, Volume 64 in the Springer Verlag Lecture Notes in Computer Science Series, 345-354 (with Carter, Wegman).
  23. Free Completely Distributive Lattices Proc. Am. Math. Soc.74, 1979, 227-228.
  24. A Fast Algorithm For Steiner Trees presented at the 10th S. E. Conference on Combinatorics, Graph Theory and Computing, Boca Raton, 1979. Also appears in Acta Informatica 15, 1981, 141-5 (with Kou, Berman).
  25. Search Within a Page JACM, Vol. 26, No.3, July 1979, 457-82 (with Strong, Chandra).
  26. Diagnosing Single Faults in Fanout-Free Combinatorial Circuits IEEE Trans. on Computers, Vol. C-28, No.11, November 1979, 863-4.
  27. A Motivation and Generalization of Scott's Notion of Continuous Lattice Proc. of the 1979 Bremen Conference on Topological and Categorical Aspects of Continuous Lattices, Springer Verlag Lecture Notes in Mathematics, No.871, 298-307.
  28. Propaedeutic to Chain-Complete Posets with Basis Proc. of the 1979 Bremen Conference on Topological and Categorical Aspects of Continuous Lattices, Springer Verlag Lecture Notes in Mathematics, No.871, 308- 14.
  29. On a Class of One-Step Majority-Logic Decodable Cyclic Codes IBM J. of R&D, Vol.24 No. 1, January 1980, 56-63 (with Lin).
  30. Fleshing Out Wire Frames IBM J. R&D, Vol.24, No. 5, September 1980, 582-597 (with Wesley). This work was also described in a Science Digest article.
  31. The Representation of Posets and Lattices by Sets Algebra Univ., 11, 1980, 173-92.
  32. On the Generation of Explicit Routing Tables Proc. Fifth International Conference on Computer Communications, Atlanta, October 1980 (with Maruyama).
  33. Uncovering Antibody Incidence Structures Math. Biosciences, 52, 1980, 141-56 (with Wohlgemuth).
  34. The Level Polynomials of the Free Distributive Lattices Discrete Mathematics, 29, 1980, 275-85.
  35. A Fragment-Cofragment Model of Antibody Incidence Structures Math. Biosciences, 53, 1981, 265-73 (with Wohlgemuth).
  36. Syndrome-Testability Can be Achieved by Circuit Modification IEEE Trans. on Computers, Vol. C-30, No. 8, August 1981, 604-6.
  37. Vocational Rehabilitation of the Severely Disabled: Voice Controlled Computer Programming Proc. 4th Ann. Conf. on Rehab. Engineering, Washington, DC, August 30-September 3, 1981, 135-6 (with Youdin and Reich).
  38. Fleshing Out Projections IBM J. of R&D, November 1981, 934-54 (with Wesley). This paper has been reprinted (pp. 387-407) in Computer Vision: Principles ed. by Rangachar Kasturi and Ramesh C. Jain, IEEE Computer Society Press, Los Alamitos, CA 1991. The results of this paper and of Fleshing Out Wire Frames were featured in a Science Digest article.
  39. An Evaluation of Local Path ID Swapping in Computer Networks IEEE Trans. on Communications, Vol. Com-29, No.3, March 1981, 329-36 (with Moss).
  40. The Weighted Syndrome Sums Approach to VLSI Testing IEEE Trans. on Computers, Vol. C-30, No.12, December 1981, 996-1000 (with Barzilai, Savir, Smith).
  41. Best Huffman Trees Acta Informatica, 16, 1981, 363-370.
  42. Extending Semilattices is Hard Algebra Universalis, 17 (1983) 406- 407.
  43. Reduced Set of Phages for Typing Salmonellae J. of Clinical Microbiology, Vol. 17, No. 2, Feb. 1983, 240-4, (with Gershman).
  44. Identifying Antigens and Antibodies in Serology Math. Biosciences, 66:273-282 (1983) (with Wohlgemuth).
  45. Intersection-Union Systems Discrete Applied Math. 6 (1983) 255-262 (with Wohlgemuth).
  46. Necessary and Sufficient Conditions for a Phenotype System to Have a Factor Union Representation Math. Biosciences, 66 (1983), 115-128.
  47. Mathematical Immunogenetics I - A Survey J. of Theoretical Biology, (1983) 102, 411-424, (with Wohlgemuth).
  48. Mathematical Immunogenetics II - Antibody Incidence Structure J. of Theoretical Biology(1983) 102, 425-437, (with Wohlgemuth).
  49. On Sets of Boolean n-Vectors with All k-Projections Surjective Acta Informatica20, 103-111 (1983) (with Chandra, Kou, Zaks).
  50. Reduced Set of Phages for Typing E-Coli J. of Dairy Science, 67 (1984), 1306-1315 (with Gershman and Hunter).
  51. Generation of Solid Models From Two-Dimensional and Three-Dimension Data a chapter in Solid Modeling by Computers, Ed. by M. S. Pickett and John W. Boyse (Plenum Publishing, 1984), 23-51 (with Wesley).
  52. Mainstream Solutions for the Problems of Disability Proc. Second IBM Corporate Technical Symposium on Employee Initiated Projects for Persons with Disabilities, White Plains, NY, October 1986.
  53. Bounding Signal Probabilities in Combinatorial Circuits IEEE Trans. on Computers, Vol. C-36, No. 10, October 1987, 1247-1251.
  54. Learning Probabilistic Prediction Functions 29th Annual Symposium on the Foundations of Computer Science(FOCS), October 24-26, 1988, pp. 110-119 (with DeSantis, Wegman).
  55. Phage Typing Set for Differentiating Staphylococcus Epidermidis Canadian J. of Microbiology, V. 34, 1988, pp. 1358-1361 (with Gershman, Hunter, Harmon, Wilson).
  56. Numerical Tic-Tac-Toe I J. of Recreational Math., Vol. 22, No. 2, 1990, pp. 114-123.
  57. Numerical Tic-Tac-Toe II J. of Recreational Math., Vol. 23, No. 3, 1990, pp. 192-200. The results in this paper and the preceding one have been featured in articles in OMNI Magazine, December 1989 and The Sciences.
  58. Making a Golden Rectangle by Paper Folding The Mathematical Gazette, Vol. 75, No. 471, March 1991, pp. 85-87. Reprinted in The Changing Shape of Geometry: Celebrating a Centure of Geometry and Geometry Teaching, ed. by Chris Pritchard, Cambridge U. Press and MAA, 2003, pp. 301-303.
  59. Bounding Fault Detection Probabilities in Combinational Circuits Journal of Electronics Testing: Theory and Applications (JETTA), 2 (1991), 315-323.
  60. Phage Typing Sets Mathematical and Computer Modeling, Volume 16, Issue 6/7, 1992, pp. 113-119 (with Gershman and Hunter).
  61. Misconceptions About The Golden Ratio The College Mathematics Journal, Vol. 23, No. 1, Jan. 1992, 2-19.
  62. Ordering D-Classes is Hard Semigroup Forum, Vol. 44 (1992) 373-375.
  63. Primes, Irreducibles and Extremal Lattices Order, 9 (1992) 265-290.
  64. Permutation Lattices Revisited Mathematical Social Sciences, 27 (1994) 59-74. Programs to download.
  65. Introduction to Algorithmic Information Theory, J. Universal Computer Science, Vol. 2, No. 5, May 28, 1996, pp. 245-269. Reference in Journal.
  66. Representation of Inclines Algebra Colloquium, (with Kim and Roush) 4:4 (1997), 461-470.
  67. An Introduction to Algorithmic Information Theory Complexity , Vol. 2/No. 4, March/April 1997, pp. 14-22.
  68. The Poset of Irreducibles: a Basis for Lattice Theory, (invited paper at ORDAL 99) to appear in a special issue of Discrete Mathematics and Theoretical Computer Science.
  69. An Overview of the Poset of Irreducibles, (invited paper at Pohang University dedication in 2000), in Combinatorial and Computational Mathematics: Present and Future, ed. by Hong, et al, World Scientific, Singapore, 2001, pp. 162-177.
  70. Book Review: The Golden Ratio, Notices of the AMS, Vol. 52, No. 3, March, 2005, pp. 344-347.
  71. A Distributed Approach to the Recognition of Geographically Located IP Devices with Romanyak and Sachenko, in Cyberspace Security and Defense: Research Issues, ed. by J. S. Kowalik, J. Gorski and A. Sachenko, NATO Sci. Series, Springer 2005, pp. 193-207.

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