Journal Papers, Book Chapters and Book Reviews

Most of my newer publications have come out as Conference Papers, so please check that section. Most of these papers are available for download at


  1. The Sad History of Random Bits,Journal of Cyber Security, January 2014, Vol. 3, No. 1, pp. 1-26.
  2. The Ternopil Educational Communication Center – A NATO Project to Integrate Regional Information Technology Resources, COMPUTING, Vol. 7, Issue 1, 2008, pp. 185-190, (with Sachenko, Voznyak, Spilchuk, Romanyak, Tuchenko, and Romanets).
  3. 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.
  4. Book Review: The Golden Ratio, Notices of the AMS, Vol. 52, No. 3, March, 2005, pp. 344-347.
  5. Information Theory, The Macropedia, Encyclopedia Britannica 2002 Edition.
  6. 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.
  7. 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.
  8. An Introduction to Algorithmic Information Theory, Complexity, Vol. 2/No. 4, March/April 1997, pp. 14-22.
  9. Representation of Inclines, Algebra Colloquium, (with Kim and Roush) 4:4 (1997), 461-470.
  10. Introduction to Algorithmic Information Theory, J. Universal Computer Science, Vol. 2, No. 5, May 28, 1996, pp. 245-269. Reference in Journal.
  11. Permutation Lattices Revisited, Mathematical Social Sciences, 27 (1994) 59-74. Programs to download.
  12. Primes, Irreducibles and Extremal Lattices, Order, 9 (1992) 265-290.
  13. Ordering D-Classes is Hard, Semigroup Forum, Vol. 44 (1992) 373-375.
  14. Misconceptions About The Golden Ratio, The College Mathematics Journal, Vol. 23, No. 1, Jan. 1992, 2-19.
  15. Phage Typing Sets Mathematical and Computer Modeling, Volume 16, Issue 6/7, 1992, pp. 113-119 (with Gershman and Hunter).
  16. Bounding Fault Detection Probabilities in Combinational Circuits, Journal of Electronics Testing: Theory and Applications (JETTA), 2 (1991), 315-323.
  17. 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.
  18. 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.
  19. Numerical Tic-Tac-Toe I, J. of Recreational Math., Vol. 22, No. 2, 1990, pp. 114-123.
  20. Phage Typing Set for Differentiating Staphylococcus Epidermidis,Canadian J. of Microbiology, V. 34, 1988, pp. 1358-1361 (with Gershman, Hunter, Harmon, Wilson).
  21. Learning Probabilistic Prediction Functions, 29th Annual Symposium on the Foundations of Computer Science(FOCS), October 24-26, 1988, pp. 110-119 (with DeSantis, Wegman).
  22. Bounding Signal Probabilities in Combinatorial Circuits, IEEE Trans. on Computers, Vol. C-36, No. 10, October 1987, 1247-1251.
  23. 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.
  24. 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).
  25. Reduced Set of Phages for Typing E-Coli, J. of Dairy Science, 67 (1984), 1306-1315 (with Gershman and Hunter).
  26. On Sets of Boolean n-Vectors with All k-Projections Surjective, Acta Informatica20, 103-111 (1983) (with Chandra, Kou, Zaks).
  27. Mathematical Immunogenetics II – Antibody Incidence Structure, J. of Theoretical Biology(1983) 102, 425-437, (with Wohlgemuth).
  28. Mathematical Immunogenetics I – A Survey, J. of Theoretical Biology, (1983) 102, 411-424, (with Wohlgemuth).
  29. Necessary and Sufficient Conditions for a Phenotype System to Have a Factor Union Representation, Math. Biosciences, 66 (1983), 115-128.
  30. Intersection-Union Systems, Discrete Applied Math. 6 (1983) 255-262 (with Wohlgemuth).
  31. Identifying Antigens and Antibodies in Serology, Math. Biosciences, 66:273-282 (1983) (with Wohlgemuth).
  32. Reduced Set of Phages for Typing Salmonellae, J. of Clinical Microbiology, Vol. 17, No. 2, Feb. 1983, 240-4, (with Gershman).
  33. Extending Semilattices is Hard, Algebra Universalis, 17 (1983) 406- 407.
  34. Best Huffman Trees, Acta Informatica, 16, 1981, 363-370.
  35. 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).
  36. 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).
  37. 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.
  38. 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).
  39. Syndrome-Testability Can be Achieved by Circuit Modification, IEEE Trans. on Computers, Vol. C-30, No. 8, August 1981, 604-6.
  40. A Fragment-Cofragment Model of Antibody Incidence Structures, Math. Biosciences, 53, 1981, 265-73 (with Wohlgemuth).
  41. The Level Polynomials of the Free Distributive Lattices, Discrete Mathematics, 29, 1980, 275-85.
  42. Uncovering Antibody Incidence Structures, Math. Biosciences, 52, 1980, 141-56 (with Wohlgemuth).
  43. On the Generation of Explicit Routing Tables, Proc. Fifth International Conference on Computer Communications, Atlanta, October 1980 (with Maruyama).
  44. The Representation of Posets and Lattices, by Sets Algebra Univ., 11, 1980, 173-92.
  45. 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.
  46. 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).
  47. 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.
  48. 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.
  49. Diagnosing Single Faults in Fanout-Free Combinatorial Circuits, IEEE Trans. on Computers, Vol. C-28, No.11, November 1979, 863-4.
  50. Search Within a Page JACM, Vol. 26, No.3, July 1979, 457-82 (with Strong, Chandra).
  51. 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).
  52. Free Completely Distributive Lattices, Proc. Am. Math. Soc.74, 1979, 227-228.
  53. 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).
  54. On The Number of Prime Implicants, Discrete Math. 24, 1978, 7-11 (with Chandra).
  55. Differential Operators and the Theory of Binomial Enumeration, J. Math. Analysis and Applications, 63, 1978, 145-155.
  56. A Mathematical Analysis of Human Leukocyte Antigen Serology, Math. Biosciences 40, 1978, 243-270 (with Nau, Woodbury, Amos).
  57. Exact and Approximate Membership Testers, Proc. 10th Ann. Symp. on Theory of Computing(SIGACT),May 1978, 59-65 (with Carter, Floyd, Gill, Wegman).
  58. Multidimensional Bin Packing Algorithms, IBM J. R&D, 21, 1977, 443-448 (with Kou).
  59. Subprojective Lattices and Projective Geometry, J. Algebra 48, 1977, 305-320 (with Petrich).
  60. Bounds on the Index and Period of a Binary Relation on a Finite Se,t Semigroup Forum 13, 1977, 253-259.
  61. Categories of Chain-Complete Posets, Theoretical Computer Science 4, 1977, 125-135.
  62. Lower Bounds on the Length of Node Sequences in Directed Graphs, Discrete Math. 16, 1976, 329-337 (with Tarjan).
  63. Bases for Chain-complete Posets, IBM J. R&D, 20, 1976, 138-147 (with Rosen).
  64. Chain-complete Posets and Directed Sets with Applications, Algebra Univ.6, 1976, 53-68.
  65. On Dedekind’s Problem: The Number of Isotone Boole an Functions II, Trans. Am. Math. Soc. 213, 1975, 373-390 (with Kleitman).
  66. The Factorization and Representation of Lattices, Trans. Am. Math. Soc. 203, 1975, 185-200.
  67. The Number of Partially Ordered Sets II, J. Korean Math. Soc., 11, April 1974, 7-17 (with Butler).
  68. Some Combinatorial Aspects of Lattice Theory, Proc. Univ. of Houston Lattice Theory Conf., 1973, 36-68.
  69. Enumeration of Finite Topologies Proc. 4th S. E. Conference on Combinatorics, Graph Theory and Computing, Boca Raton, 1973, 169-184 (with Butler).
  70. The Number of Maximal Subgroups of the Semigroup of Binary Relations II, Kyungpook Math J., 12, December 1972, 199-211 (with Butler).
  71. The Number of Maximal Subgroups of the Semigroup of Binary Relations, Kyungpook Math J., 12, June 1972, 1-8 (with Butler).
  72. Indempotents and Product Representations with Applications to the Semigroup of Binary Relations, Semigroup Forum 5, 1972, 95-119.
  73. The Schutzenberger Group of an H-Class in the Semigroup of Binary Relations, Semigroup Forum 5, 1972, 45-53 (with Brandon, Hardy).
  74. Cardinalities of D-Classes in Bn, Semigroup Forum 4, 1972, 341-344 (with Brandon, Butler, Hardy).