¶¡ÏãÔ°AV

The Papers of Tom C. Brown,
Department of Mathematics, ¶¡ÏãÔ°AV

Notice: In order to compile these LaTeX files, you will also need the Bibliography file.

• On Double 3-term Arithmetic Progressions [tex] [pdf]
  Tom Brown, Veselin Jungić, and Andrew Poelstra, On double 3-term arithmetic progressions, INTEGERS - Elect. J. Combin. Number Theory 14 (2014), #A43.
• On abelian and additive complexity in infinite words [tex] [pdf]
  Hayri Ardal, Tom Brown, Veselin Jungić, and Julian Sahasrabudhe, On abelian and additive complexity in infinite words, INTEGERS - Elect. J. Combin. Number Theory 12 (2012), #A21.
• Approximations of additive squares in infinite words [tex] [pdf]
  T.C. Brown, Approximations of additive squares in infinite words, INTEGERS - Elect. J. Combin. Number Theory 12 (2012), A22.
• Chaotic orderings of the rationals and reals [tex] [pdf]
  Hayri Ardal, Tom Brown, and Veselin Jungić, Chaotic orderings of the rationals and reals, Amer. Math. Monthly 118 (2011), 921--925.
• On Finitely Generated Idempotent Semigroups [tex] [pdf]
  T.C. Brown and Earl Lazerson, On finitely generated idempotent semigroups, Semigroup Forum 78 (2009), 183--183.
• Bounds on some van der Waerden numbers [tex] [pdf]
  T.C. Brown, Bruce M. Landman, and Aaron Robertson, Bounds on some van der Waerden numbers, J. Combin. Theory Ser. A.
• A partition of the non-negative integers, with applications to Ramsey Theory [tex] [pdf] [notes]
  T.C. Brown, A partition of the non-negative integers, with applications to Ramsey theory, Discrete Mathematics and its Applications (Proceedings of the International Conference on Discrete Mathematics and its Applications, Amrita Vishwa Vidyapeetham, Ettimadai Coimbatore, India), Narosa Publishing House, 2006, pp. 79--87.
• A coloring of the non-negative integers, with applications [tex] [pdf] [notes]
  T.C. Brown, A partition of the non-negative integers, with applications, INTEGERS - Elect. J. Combin. Number Theory 5 (2005), no. 2, A2, (Proceedings of the Integers Conference 2003 in Honor of Tom Brown's Birthday).
• Almost disjoint families of 3-term arithmetic progressions [tex] [pdf]
  Hayri Ardal, Tom Brown, and Peter A.B. Pleasants, Almost disjoint families of 3-term arithmetic progressions, J. Combin. Theory Ser. A 109 (2005), 75--90.
• A Simple Proof of Lerch's Formula [tex] [pdf]
  T.C. Brown and Jan Manuch, A simple proof of Lerch's formula, Proceedings of the Eleventh International Conference on Fibonacci Numbers and their Applications. Numer. 194 (2009), 91--93.
• Progressions of Squares [tex] [pdf]
  T.C. Brown, A.R. Freedman, and P. J.-S. Shiue, Progressions of squares, Australas. J. Combin. 27 (2004), 187--192.
• On the partition function of a finite set [tex] [pdf]
  Tom C. Brown, Wun-Seng Chou, and Peter J.-S. Shiue, On the partition function of a finite set, Australas. J. Combin. 27 (2003), 193--204.
• Monochromatic structures in colorings of the positive integers and the finite subsets of the positive integers [tex] [pdf]
  T.C. Brown, Monochromatic structures in colorings of the positive integers and the finite subsets of the positive integers, 15th MCCCC (Las Vegas, NV, 2001). J. Combin. Math. Combin. Comput. 46 (2003), 141--153.
• On the canonical version of a theorem in Ramsey Theory [tex] [pdf]
  T.C. Brown, On the canonical version of a theorem in Ramsey theory, Special Issue on Ramsey Theory, Combinatorics, Probability and Computing 12 (2003), 513--514.
• Applications of standard Sturmian words to elementary number theory [tex] [pdf]
  T.C. Brown, Applications of standard Sturmian words to elementary number theory., WORDS (Rouen, 1999). Theoret. Comput. Sci. 273 (2002), no. 1--2, 5--9.
• On the history of van der Waerden's theorem on arithmetic progressions [tex] [pdf]
  T.C. Brown and P.J.-S. Shiue, On the history of van der Waerden's theorem on arithmetic progressions, Tamkang J. Math. 32 (2001), no. 4, 335--341.
• Monochromatic Forests of Finite Subsets of $\mathbb{N}$ [tex] [pdf]
  T.C. Brown, Monochromatic forests of finite subsets of $N$, INTEGERS - Elect. J. Combin. Number Theory 0 (2000), A4.
• On a Certain Kind of Generalized Number-Theoretical Möbius Function [tex] [pdf]
  T.C. Brown, C. Hsu Leetsch, Jun Wang, and Peter J.-S. Shiue, On a certain kind of generalized number-theoretical Moebius function, Math. Scientist 25 (2000), 72--77.
• On the Set of Common Differences in van der Waerden's Theorem on Arithmetic Progressions [tex] [pdf] [notes]
  T.C. Brown, R.L. Graham, and B.M. Landman, On the set of common differences in van der Waerden's theorem on arithmetic progressions, Canad. Math. Bull. 42 (1999), 25--36.
• Monochromatic Arithmetic Progressions With Large Differences [tex] [pdf]
  T.C. Brown and Bruce M. Landman, Monochromatic arithmetic progressions with large differences, Bull. Austral. Math. Soc. 60 (1999), no. 1, 21--35.
• Monochromatic Arithmetic Forests [tex] [pdf]
  T.C. Brown, Monochromatic arithmetic forests, Paul Erdos and His Mathematics (A. Sali, M. Simonovits, and V.T. Sós, eds.), Janos Bolyai Mathematical Society, Budapest, Hungary, 1999, pp. 42--44.
• A Pseudo Upper Bound for the van der Waerden Function [tex] [pdf]
  T.C. Brown, A pseudo upper bound for the van der Waerden function, J. Combin. Theory Ser. A 87 (1999), 233--238.
• Sequences with Translates Containing Many Primes [tex] [pdf]
  T.C. Brown, P. J.-S. Shiue, and X.Y. Yu, Sequences with translates containing many primes, Canad. Math. Bull. 41 (1998), 15--19.
• Arithmetic Progressions in Sequences With Bounded Gaps [tex] [pdf]
  T.C. Brown and D.R. Hare, Arithmetic progressions in sequences with bounded gaps, J. Combin. Theory Ser. A 77 (1997), 222--227.
• Monochromatic Homothetic Copies of $\{1, 1+s, 1+s+t\}$ [tex] [pdf]
  T.C. Brown, Bruce M. Landman, and Marni Mishna, Monochromatic homothetic copies of $\lbrace s, 1+s, 1+s+t \rbrace$ , Canad. Math. Bull. 40 (1997), 149--157.
• The Ramsey property for collections of sequences not containing all arithmetic progressions [tex] [pdf]
  T.C. Brown and Bruce M. Landman, The Ramsey property for collections of sequences not containing all arithmetic progressions, Graphs and Combinatorics 12 (1996), 149--161.
• Squares of Second-Order Linear Recurrence Sequences [tex] [pdf]
  T.C. Brown and P.J.-S. Shiue, Squares of second-order sequences, Fib. Quart. 33 (1995), 352--356.
• Irrational Sums [tex] [pdf] [notes]
  T.C. Brown and P.J.-S. Shiue, Irrational sums, Rocky Mountain J. Math. 25 (1995), 1219--1223.
• Sums of Fractional Parts of Integer Multiples of an Irrational [tex] [pdf] [notes]
  T.C. Brown and P.J.-S. Shiue, Sums of fractional parts of integer multiples of an irrational, J. Number Theory 50 (1995), 181--192.
• A Simple Proof of a Remarkable Continued Fraction Identity [tex] [pdf]
  P.G. Anderson, T.C. Brown, and P.J.-S. Shiue, A simple proof of a remarkable continued fraction identity, Proc. Amer. Math. Soc. 123 (1995), 2005--2009.
• Powers of Digital Sums [tex] [pdf]
  T.C. Brown, Powers of digital sums, Fib. Quart. 32 (1994), 207--210.
• A Remark Related to the Frobenius Problem [tex] [pdf]
  T.C. Brown and P.J.-S. Shiue, A remark related to the Frobenius problem, Fib. Quart. 31 (1993), 32--36.
• Descriptions of the Characteristic Sequence of an Irrational [tex] [pdf] [notes]
  T.C. Brown, Descriptions of the characteristic sequence of an irrational, Canad. Math. Bull. 36 (1993), 15--21.
• Some Sequences Associated with the Golden Ratio [tex] [pdf]
  T.C. Brown and A.R. Freedman, Some sequences associated with the golden ratio, Fib. Quart. 29 (1991), 157--159.
• A Characterization of the Quadratic Irrationals [tex] [pdf]
  T.C. Brown, A characterization of the quadratic irrationals, Canad. Math. Bull. 34 (1991), 36--41.
• Monochromatic Solutions to Equations with Unit Fractions [tex] [pdf]
  T.C. Brown and V. Rödl, Monochromatic solutions to equations with unit fractions, Bull. Aus. Math. Soc. 43 (1991), 387--392.
• Quasi-Progressions and Descending Waves [tex] [pdf] [notes]
  T.C. Brown, P. Erdős, and A.R. Freedman, Quasi-progressions and descending waves, J. Combin. Theory Ser. A 53 (1990), 81--95.
• Cancellation in Semigroups in Which $x^2 = x^3$ [tex] [pdf]
  T.C. Brown, Cancellation in semigroups in which $x^2 = x^3$, Semigroup Forum 41 (1990), 49--53.
• The Uniform Density of Sets of Integers and Fermat's Last Theorem [tex] [pdf]
  T.C. Brown and A.R. Freedman, The uniform density of sets of integers and Fermat's Last Theorem, C.R. Math. Rep. Acad. Sci. Canad. 12 (1990), 1--6.
• Small Sets Which Meet All the $k(n)$-Term Arithmetic Progressions in the Interval $[1,n]$ [tex] [pdf]
  T.C. Brown and A.R. Freedman, Small sets which meet every $f(n)$-term arithmetic progressions in the interval $[1, n]$, J. Combin. Theory Ser. A 51 (1989), 244--249.
• Arithmetic Progressions in Lacunary Sets [tex] [pdf] [notes]
  T.C. Brown and A.R. Freedman, Arithmetic progressions in lacunary sets, Rocky Mountain J. Math. 17 (1987), no. 3, 587--596.
• Affine and Combinatorial Binary $m$-Spaces [tex] [pdf]
  T.C. Brown, Affine and combinatorial binary $m$-spaces, J. Combin. Theory Ser. A 38 (1985), 25--34.
• Monochromatic Affine Lines in Finite Vector Spaces [tex] [pdf]
  T.C. Brown, Monochromatic affine lines in finite vector spaces, J. Combin. Theory Ser. A 38 (1985), 35--41.
• Quantitative Forms of a Theorem of Hilbert [tex] [pdf]
  T.C. Brown, F.R.K. Chung, P. Erdős, and R.L. Graham, Quantitative forms of a theorem of Hilbert, J. Combin. Theory Ser. A 38 (1985), 210--216.
• Lines Imply Spaces in Density Ramsey Theory [tex] [pdf] [notes]
  T.C. Brown and J.P. Buhler, Lines imply spaces in density Ramsey theory, J. Combin. Theory Ser. A 36 (1984), 214--220.
• Common Transversals for Partitions of a Finite Set [tex] [pdf] [notes]
  T.C. Brown, Common transversals for partitions of a finite set, Discrete Math. 51 (1984), 119--124.
• A Graph-Theoretic Conjecture Which Implies Szemerédi's Theorem [tex] [pdf]
  T.C. Brown, A graph-theoretic conjecture which implies Szemerédi's theorem, Bull. Istanbul Tech. Univ. 37 (1984), 59--63.
• Some Quantitative Aspects of Szemerédi's Theorem Modulo $n$ [tex] [pdf]
  T.C. Brown, Some quantitative aspects of Szemerédi's theorem modulo $n$, congressus Numerantium 43 (1984), 169--174.
• Probabilistic Prospects of Stackelberg Leader and Follower [tex] [pdf]
  Ahmet Alkan, T.C. Brown, and Murat Sertel, Probabilistic prospects of Stackelberg leader and follower, J. Optimization Theory and Applications 39 (1983), 379--389.
• Common Transversals for Three Partitions [tex] [pdf]
  T.C. Brown, Common transversals for three partitions, Bogazici University J. 10 (1983), 47--49.
• An Application of Density Ramsey Theory to Transversal Theory [tex] [pdf]
  T.C. Brown, An application of density Ramsey theory to transversal theory, Bogazici University J. 10 (1983), 41--46.
• Behrend's Theorem for Dense Subsets of Finite Vector Spaces [tex] [pdf] [notes]
  T.C. Brown and J.P. Buhler, Behrend's theorem for dense subsets of finite vector spaces, Canad. J. Math. 35 (1983), 724--734.
• A Density Version of a Geometric Ramsey Theorem [tex] [pdf] [notes]
  T.C. Brown and J.P. Buhler, A density version of a geometric Ramsey theorem, J. Combin. Theory Ser. A 25 (1982), 20--34.
• Common Transversals [tex] [pdf] [notes]
  T.C. Brown, On van der Waerden's theorem and a theorem of Paris and Harrington, J. Combin. Theory Ser. A 30 (1981), 108--111.
• On Homogeneous Cubes [tex] [pdf] [notes]
  T.C. Brown, On homogeneous cubes, Bogazici University J. 6 (1978), 13--16.
• On the Density of Sets Containing No $k$-Element Arithmetic Progression of a Certain Kind [tex] [pdf]
  B. Alspach, T.C. Brown, and P. Hell, On the density of sets containing no $k$-element arithmetic progressions of a certain kind, J. London Math. Soc. (2) 13 (1976), 226--234.
• Common Transversals [tex] [pdf]
  T.C. Brown, Common transversals, J. Combin. Theory Ser. A 21 (1976), 80--85.
• Variations on van der Waerden's and Ramsey's Theorems [tex] [pdf] [notes]
  T.C. Brown, Variations on van der Waerden's and Ramsey's theorems, Amer. Math. Monthly 82 (1975), 993--995.
• A Proof of Sperner's Lemma via Hall's Theorem [tex] [pdf] [notes]
  T.C. Brown, A proof of Sperner's lemma via Hall's theorem, Proc. Camb. Philos. Soc. 78 (1975), 387.
• Behrend's Theorem for Sequences Containing No $k$-Element Arithmetic Progression of a Certain Type [tex] [pdf] [notes]
  T.C. Brown, Behrend's theorem for sequences containing no $k$-element arithmetic progression of a certain type, J. Combin. Theory Ser. A 18 (1975), 352--356.
• An Interesting Combinatorial Method in the Theory of Locally Finite Semigroups [tex] [pdf]
  T.C. Brown, An interesting combinatorial method in the theory of locally finite semigroups, Pacific J. Math. 36 (1971), 285--289.
• On $N$-Sequences [tex] [pdf]
  T.C. Brown, On $N$-sequences, Math. Magazine 44 (1971), 89--92.
• Is There a Sequence on Four Symbols in Which No Two Adjacent Segments Are Permutations of One Another? [tex] [pdf]
  T.C. Brown, Is there a sequence on four symbols in which no two adjacent segments are permutations of one other?, American Math. Monthly 78 (1971), 886--888.
• On Locally Finite Semigroups [tex] [pdf]
  T.C. Brown, On locally finite semigroups (In Russian), Ukraine Math. J. 20 (1968), 732--738.
• A Semigroup Union of Disjoint Locally Finite Subsemigroups Which is Not Locally Finite [tex] [pdf]
  T.C. Brown, A semigroup union of disjoint locally finite subsemigroups which is not locally finite, Pacific J. Math. 22 (1967), 11--14.
• On the Finiteness of Semigroups in Which $x^r = x$ [tex] [pdf]
  T.C. Brown, On the finiteness of semigroups in which $x^r = r$, Proc. Cambridge Philos. Soc. 60 (1964), 1028--1029.

This page was created by Andrew Poelstra and Graham Banero, Department of Mathematics, ¶¡ÏãÔ°AV