The mathematics of Bruce Rothschild

A review is given of some of the mathematical research of Bruce Rothschild, emphasizing his results in combinatorial theory, especially that part known as Ramsey Theory. Special emphasis is given to the Graham-Rothschild Parameter Sets Theorem, its consequences, and some extensions.

[1]  Bruce Rothschild,et al.  Induced Partition Theorems , 1982, J. Comb. Theory, Ser. A.

[2]  B. Rothschild,et al.  An application of Ramsey's Theorem to the Banach Contraction Principle , 2001 .

[3]  Bruce Rothschild,et al.  Lower bounds on blocking sets. , 1985 .

[4]  R. Graham,et al.  Ramsey's theorem for $n$-dimensional arrays , 1969 .

[5]  Vojtěch Rödl,et al.  Mathematics of Ramsey Theory , 1991 .

[6]  Paul Erdös,et al.  Euclidean Ramsey Theorems I , 1973, J. Comb. Theory, Ser. A.

[7]  Bruce Rothschild,et al.  The Decomposition of Graphs into a Finite Number of Paths , 1965, Canadian Journal of Mathematics.

[8]  R. Graham,et al.  Are There n + 2 Points in E n With Odd Integral Distances? , 1974 .

[9]  Bruce Rothschild,et al.  On Characterizing Subspaces , 1980, J. Comb. Theory, Ser. A.

[10]  Bruce Rothschild,et al.  A canonical restricted version of van der waerden’s theorem , 1987, Comb..

[11]  B. Rothschild,et al.  Sex, drugs and matrices: Mathematical prediction of HIV infection , 1988 .

[12]  D. Hilbert.  Ueber die Irreducibilität ganzer rationaler Functionen mit ganzzahligen Coefficienten. , 1892 .

[13]  Bruce Rothschild,et al.  Inferring protein interactions from phylogenetic distance matrices , 2003, Bioinform..

[14]  Daniel J. Kleitman,et al.  The number of semigroups of order n , 1976 .

[15]  B. Rothschild,et al.  On Two Commodity Network Flows , 1966, Oper. Res..

[16]  B. Rothschild,et al.  Asymptotic enumeration of partial orders on a finite set , 1975 .

[18]  B. Rothschild,et al.  Feasibility of Two Commodity Network Flows , 1966, Oper. Res..

[19]  Neil Hindman,et al.  An infinitary extension of the Graham–Rothschild Parameter Sets Theorem , 2006 .

[20]  Ph. G. Kolaitis,et al.  _{+1}-free graphs: asymptotic structure and a 0-1 law , 1987 .

[21]  Ronald L. Graham,et al.  A short proof of van der Waerden’s theorem on arithmetic progressions , 1974 .

[22]  Primitive subalgebras of exceptional Lie algebras , 1971 .

[23]  P. Erdös,et al.  INTERSECTION THEOREMS FOR SYSTEMS OF FINITE SETS , 1961 .

[24]  James E. Baumgartner,et al.  A Short Proof of Hindman's Theorem , 1974, J. Comb. Theory, Ser. A.

[25]  Bruce Rothschild,et al.  A Generalization of the Erdös-Ko-Rado Theorem on Finite Set Systems , 1973, J. Comb. Theory, Ser. A.

[26]  P. Erdos,et al.  On chromatic number of graphs and set-systems , 1966 .

[27]  Joel H. Spencer.  Restricted Ramsey Configurations , 1975, J. Comb. Theory, Ser. A.

[28]  P. Erdos,et al.  On chromatic number of graphs and set-systems , 1966 .

[29]  Neil Hindman,et al.  Finite Sums from Sequences Within Cells of a Partition of N , 1974, J. Comb. Theory, Ser. A.

[30]  H. Prömel,et al.  A RESTRICTED VERSION OF HALES–JEWETT'S THEOREM , 1984 .

[31]  Daniel J. Kleitman,et al.  Configurations Maximizing the Number of Pairs of Hamming-Adjacent Lattice Points , 1971 .

[32]  R. Graham,et al.  Ramsey’s theorem for $n$-parameter sets , 1971 .

[33]  Bruce Rothschild.  Characterizing k-Flats in Geometric Designs , 1976, J. Comb. Theory, Ser. A.

[34]  Nathan Linial,et al.  Incidence Matrices of Subsets—A Rank Formula , 1981 .

[35]  R. Graham,et al.  Some Recent Developments in Ramsey Theory , 1975 .

[36]  Zoltán Füredi,et al.  Induced subgraphs of given sizes , 1999, Discret. Math..

[37]  Frank Plumpton Ramsey,et al.  On a Problem of Formal Logic , 1930 .

[38]  J. Spencer.  Ramsey Theory , 1990 .

[39]  Ron Graham,et al.  Ramsey's Theorem for a Class of Categories. , 1972 .

[40]  D. J. Kleitman,et al.  A phase transition on partial orders , 1979 .

[41]  Andrew B. Whinston,et al.  A matching theorem for graphs , 1970 .

[42]  D. Kleitman,et al.  The number of finite topologies , 1970 .

[43]  Bruce Rothschild,et al.  A generalization of Kaplansky's game , 1972, Discret. Math..

[44]  Ph. G. Kolaitis,et al.  Asymptotic enumeration and a 0-1 law for $m$-clique free graphs , 1985 .

[45]  C. St. J. A. Nash-Williams,et al.  Decomposition of Graphs into Two-Way Infinite Paths , 1963, Canadian Journal of Mathematics.

[46]  Bruce Rothschild,et al.  Characterizing Finite Subspaces , 1974, J. Comb. Theory, Ser. A.

[47]  Saharon Shelah,et al.  Primitive recursive bounds for van der Waerden numbers , 1988 .

[48]  B. Rothschild,et al.  Every graph is contained in a sparsest possible balanced graph , 1985, Mathematical Proceedings of the Cambridge Philosophical Society.

[49]  I. Kríz.  Permutation groups in Euclidean Ramsey theory , 1991 .

[50]  V. Rödl,et al.  All triangles are Ramsey , 1986 .

[51]  Neil Hindman,et al.  Algebra in the Stone-Cech Compactification: Theory and Applications , 1998 .

[52]  Bruce Rothschild,et al.  On triangulations of the convex hull ofn points , 1985, Comb..

[53]  Bernd Voigt,et al.  Graham-Rothschild Parameter Sets , 1990 .

[54]  R L Graham,et al.  Ramsey's Theorem for a Class of Categories. , 1972, Proceedings of the National Academy of Sciences of the United States of America.

[55]  R. Rado,et al.  Studien zur Kombinatorik , 1933 .

[56]  Paul Erdös,et al.  Partition Theorems for Subsets of Vector Spaces , 1976, J. Comb. Theory, Ser. A.

[57]  R. Collier,et al.  Appendix: a model of plaque formation. , 1981, Gene.

[58]  Maximal Two-Way Flows , 1967 .

[59]  Walter Deuber.  A generalization of Ramsey's theorem for regular trees , 1975 .

[60]  Timothy J. Carlson,et al.  Some unifying principles in Ramsey theory , 1988, Discret. Math..

[61]  G. Rota,et al.  Studies in combinatorics , 1980 .