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Herbert John Ryser

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Created Feb 2 2006 - 1:59pm

1923-1985

Herbert J. Ryser


Herbert J. Ryser was born on July 28, 1923 in Milwaukee, Wisconsin to Fred G. and Edna (Huels) Ryser. He attended the University of Wisconsin, receiving a BA. in 1945, an MA. in 1947, and a Ph.D. in 1948. His doctoral thesis "Rational Vector Spaces" was written under the direction of C. J. Everett and Cyrus C. MacDuffee [0]. He then spent the year 1948-1949 at the Institute for Advanced Study in Princeton.

In 1949 he was appointed assistant professor at Ohio State. He was promoted to associate professor in 1952 and to professor in 1955. His presence at Ohio State together with Marshall Hall [0] established a tradition of excellence in combinatorics in the department. While at Ohio State, Ryser directed four Ph.D. students [0].

In 1962 Ryser accepted an appointment at Syracuse University, then in 1967 he moved to California Institute of Technology, where he spent the rest of his life.

Ryser is widely regarded as one of the major figures in combinatorics in the 20th century. Already in his final year of graduate studies at Wisconsin, he collaborated with R. H. Bruck to prove the famous Bruck-Ryser theorem, which states that there are no projective planes of order n congruent to 1 or 2 mod 4, if n has an odd power prime factor congruent to 3. To date this is the only general nonexistence theorem for finite projective planes. In 1950 he and S. Chowla extended the nonexistence theorem to symmetric block designs. Later he found a short and elegant proof of this theorem using the Witt cancellation law.

Ryser contributed to many different parts of combinatorics, especially to the theory of combinatorial designs, finite set systems, and the permanent and other combinatorial functions. His seminal book "Combinatorial Mathematics" in the MAA Carus Monograph series is a classic which has enticed many young mathematics students into this area. He was a master expositor and a great teacher, winning several teaching awards at Caltech. He directed 12 Ph.D. students [1].

Ryser served as editor of the Journal of Combinatorial Theory, Linear and Multilinear Algebra, and the Journal of Algebra for many years. He also participated in the Visiting Lecturers' Program of the MAA for over 10 years.

He died on July 12, 1985 in Pasadena.

BIBLIOGRAPHY OF HERBERT J. RYSER

  1. Variations of vector inequalities, Amer. Math. Monthly 52(1945), 52.
  2. The Gram matrix and Hadamard theorem (with C J Everett) Amer. Math. Monthly 53(1946), 21-23.
  3. The nonexistence of certain finite projective planes (with R. H. Bruck), Canad. J. Math. 1(1949) 88-93.
  4. Rational vector spaces I ( vs th C. J. Everett) Duke Math. J. 16(1949), 553-570.
  5. Rational vector spaces II with C. J. Everett) Duke Math. J. 17( 1950), 135-145.
  6. Combinatorial problems (with S Chowla Canad. J. Math., 2(1950), 93-99.
  7. A note on a combinatorial problem, Proc. Amer. Math Soc. 1(1950), 422-424.
  8. A combinatorial theorem with an application to latin rectangles, Proc. Amer. Math. Soc. 2(1951). 550-552,
  9. Cyclic incidence matrices (with M. Hall), Canad J. Math. 3 (1951), 495-502.
  10. Matrices with integer elements in combinatorial investigations, Amer. J. Math. 74(1952), 769-773.
  11. Systems of distinct representatives (with H. B. Mann), Amer. Math. Monthly 60(1953), 397-401.
  12. Normal completions of incidence matrices (with M. Hall), Amer. J. Math. 76(1954), 581-589.
  13. Geometries and incidence matrices, Amer. Math. Monthly (Slaught Papers No. 4), 62, II(1955), 25-31.
  14. Maximal determinants in combinatorial investigations, Canad. J. Math. 8(1956), 245-249.
  15. Combinatorial properties of matrices of zeros and ones, Canad. J. Math. 9(1957), 371-377.
  16. The term rank of a matrix, Canad. J. Math. 10(1958), 57-65.
  17. Inequalities of compound and induced matrices with applications to combinatorial analysis. Illinois J. Math. 2(1958 ), 240-253.
  18. Compound and induced matrices in combinatorial analysis, in "Proc. Sympos. Appl. Math.," Vol. 10, pp. 149-167, Amer. Math. Soc., Providence, RI, 1960.
  19. Traces of matrices of zeros and ones, Canad. J. Math. 12(1960), 463-476.
  20. Traces, term ranks, widths and heights (with D. R. Fulkerson ), IBM J. Res. Develop. 4(1960), 455-459.
  21. Matrices of zeros and ones, Bull. Amer. Math. Soc. 66 (1960), 442-464.
  22. Widths and heights of (0, 1)-matrices (with D. R. Fulkerson), Canad. J. Math. 13(1961), 239-255.
  23. Multiplicities and minimal widths for (0, 1)-matrices (with D. R. Fulkerson), Canad. J. Math. 14 (1962), 498-508.
  24. Width sequences for special classes of (0, 1)-matrices (with D. R. Fulkerson), Canad. J. Math. 15(1963), 371-396.
  25. "Combinatorial Mathematics," Carus Math. Monograph No. 14, Math. Assoc. of Amer., Wiley, New York, 1963.
  26. Matrices of zeros and ones in combinatorial mathematics, in "Recent Advances in Matrix Theory," pp. 103-124, Univ. of Wisconsin, Madison. 1964.
  27. Matrix factorizations of determinants and permanents (with W. B. Jurkat), J. Algebra 3(1966), 1-27.
  28. Some recent problems in combinatorial mathematics, in "Proceedings of IFIP Congress 65," Vol. 2. pp. 494-496, 1966.
  29. "Combinatorial Mathematics," Russian translation by K. A. Ribnikov of Carus Math. Monograph No. 14, Moscow, 1966.
  30. Term ranks and permanents of nonnegative matrices (with W. B. Jurkat), J. Algebra 5(1967), 342-357.
  31. Neuere Probleme in der Kombinatorik (prepared by D. W. Müller), in Vorträge uuml;ber Kombinatorik, Oberwolfach, 1967, pp.69-91.
  32. Extremal configurations and decomposition theorems I (with W. B. Jurkat), J. Algebra 8(1968), 194-222.
  33. An extension of a theorem of de Bruijn and Erdös on combinatorial designs, J. Algebra 10(1968), 246-261.
  34. Permanents and systems of distinct representatives, in "Combinatorial Mathematics and Its Applications," pp. 55-70, Univ. of North Carolina, Chapel Hill, 1969.
  35. Combinatorial configurations, SIAM J. Appl. Math. 17(1969), 593-602.
  36. Combinatorial designs and related systems (with W. G. Bridges), J. Algebra 13(1969), 432-446.
  37. "Mathématiques Combinatories," French translation by P. Camion of Carus Math. Monograph No. 14, Dunod, Paris, 1969.
  38. A generalization of the matrix equation A2= J, Linear Algebra Appl. 3(1970), 451-460.
  39. New types of combinatorial designs, in "Proceedings. Int. Congress Math., Nice," Vol. 3, pp.235-239, 1971.
  40. Symmetric designs and related configurations, J. Combin. Theory Ser. A 12(1972), 98-111.
  41. A fundamental matrix equation for finite sets, Proc. Amer. Math. Soc. 34(1972), 332-336.
  42. Block designs with repeated blocks (with J. H. van Lint). Discrete Math. 3 1972), 381-396.
  43. Intersection properties of finite sets. J. Combin. Theory Ser. A 14(1973), 79-92.
  44. Analogs of a theorem of Schur on matrix transformations, J. Algebra 25(1973), 176-184.
  45. Variants of (v, k, l)-designs, "A Survey of Combinatorial Theory," pp. 377-384. North Holland, Atusterdam, 1973.
  46. Indeterminates and incidence matrices, Linear and Multilinear Algebra 1(1973), 149-157.
  47. Variants of cyclic difference sets. Proc. Amer. Math. Soc. 41(1973), 45-50.
  48. Subsets of a finite set that intersect each other in at most one element, J. Combin. Theory Ser. A 17(1974), 59-77.
  49. A theorem on block designs, J. Combin. Theory Ser. A 17(1974), 125-128.
  50. Indeterminates and incidence matrices, in "Combinatorics," Math. Centre Tracts Vol 55, pp. 3-17, Mathematisch Centrum, Amsterdam, 1974.
  51. The formal incidence matrix, Linear and Multilinear Algebra 3(1975), 99-104.
  52. Intersection properties of finite sets, in "Colloquio Internazionale sulle Teorie Combinatorie," Vol. 2. pp. 327-334, Accademia Nazionale dei Lincei, Rome, 1976.
  53. The factors of a design matrix, J. Combin. Theory Ser. A 22(1977), 181-193.
  54. In memoriam. D. Ray Fulkerson, 1924-1976, J. Combin. Theory Ser. B 23(1977), 1-2.
  55. Combinatorial matrix theory, in "Studies in Combinatorics," Vol. 17 (Gian-Carlo Rota, Ed.), pp. 1-21, Math Assoc. of Amer., New York, 1978.
  56. A theorem in combinatorial matrix theory, Linear Algebra Appl. 29(1980), 451-458.
  57. Matrices and set intersections, Linear Algebra Appl. 37(1981), 267-275.
  58. The existence of symmetric block designs, J. Combin. Theory Ser. A 32(1982), 103-105.
  59. Set intersection matrices, J. Combin. Theory Ser. A 32(1982), 162-177.
  60. "Combinatorial Mathematics," Chinese translation by Li Qiao of Carus Math. Monograph No. 14, China, 1983.
  61. Matrices and set differences, Discrete Math. 49(1984), 169-173.
  62. "Enumeration and Design" (D. M Jackson and S. A. Vanstone, Eds.), pp. 285-295, Academic Press, Canada, 1984.
  63. A new look at the optimal assignment problem, Linear Algebra Appl. 66(1985), 113-211.
  64. Combinatorial properties of matrices of zeros and ones, reprint of Canad. J. Math. 9(1957), 371-377. in "Classic Papers in Combinatorics" (I. Gessel and G. C. Rota, Eds.), pp. 269-275, Birkhauser, Boston, 1987.
  65. Classes of matrices associated with the optimal assignment problem, (with R. A. Brualdi, Linear Algebra Appl. 81(1986), 1-17.

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