# The Papers of Tom C. Brown,

Department of Mathematics, Simon Fraser University

**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, Simon Fraser University