 about aaron

Professor of Math
Colgate University
Department of Mathematics
Hamilton, NY 13346
+1 315.228.7227I will be on leave for the 201718 school year.
Does research in combinatorics, specifically Ramsey theory.
(my c.v.)
 publications

 Ramsey Theory

Bruce Landman and I just finished overhauling our book
Ramsey Theory on the Integers.
More info is available at:
 AMS (publisher)
 Amazon.com
 Integers

I am the associate managing editor for the journal INTEGERS, which publishes research papers in combinatorial number theory,
as popularized by Paul Erdős.
Publications
All articles ©19982018
 Submitted/To Appear
 The Determination of 2color Zerosum Generalized Schur Numbers
(WITH BIDISHA ROY AND SUBHA SARKAR)
submitted  Zerosum Generalized Schur Numbers
submitted  Zerosum Analogues of van der Waerden's Theorem on
Arithmetic Progressions
submitted  Down the Large Rabbit Hole
to appear in Rocky Mountain J. Math  On the Distribution of Monochromatic Complete Subgraphs and
Arithmetic Progressions
(WITH WILLIAM CIPOLLI AND MARIA DASCALU)
submitted  Rethinking Paleolithic Voyaging to the Offshore Islands in the
Mediterranean Sea
(WITH ALBERT AMMERMAN, JAY NOLLER, OFER BARYOSEF, MARCELLO
MANNINO, ANDREW MOORE, JEANDENIS VIGNE, AND JOAO ZILHAO)
submitted  2016
 Intermingled Ascending Wave mSets
(WITH CAITLIN CREMIN, WILL DANIEL, and QUER XIANG),
Discrete Math 339 (2016), 560563.  A Probabilistic Threshold for Monochromatic Arithmetic Progressions,
JCTA 137 (2016), 7987.  2014
 2013
 2011
 2010
 2009
 2008
 Bounds on Some van der Waerden Numbers
(with Tom Brown and Bruce Landman), JCTA 115 (7), 13041309.  Some Two Color, Four Variable Rado Numbers
(with Kellen Myers), Adv. Applied Math 41 (2), 214226.  On the Asymptotic Minimum Number of Monochromatic 3Term APs
(with Pablo Parrilo and Dan Saracino), JCTA 115 (1), 185192.  2007
 Avoiding Monochromatic Sequences with Special Gaps
(with Bruce Landman), SIAM J. Disc. Math. 21 (3), 794801.  A Method for Quantifying Rotational Symmetry
(with Frank Frey and Michael Bukoski), New Phytologist 175 (4), 785791.
Note: This is an ecology paper and not a combinatorics paper.  Two Color Offdiagonal Radotype Numbers
(with Kellen Myers), El. J. of Comb. 14(1), R53.  On Monochromatic Ascending Waves
(with Tim LeSaulnier), in Combinatorial Number Theory, de Gruyter
Proceedings in Mathematics Series.  Refined Restricted Involutions
(with Emeric Deutsch and Dan Saracino), European J. of Comb. 28, 481498.  2006
 2005
 2004
 2003
 2002
 Refined Restricted Permutations
(with Dan Saracino and Doron Zeilberger), Annals of Comb. 6, 427444.  Refined Restricted Permutations Avoiding Subsets of Patterns of Length 3
(with Toufik Mansour), Annals of Comb. 6, 407418.  On Generalized Van der Waerden Triples
(with Bruce Landman), Disc. Math 256, 279290.  New Lower Bound Formulas for Some Multicolored Ramsey Numbers
El. J. of Comb. 9(1), R13.  2001
 Permutations Restricted by Two Distinct Patterns of Length Three
Adv. in Applied Math 27, 548561.  OffDiagonal Generalized Schur Numbers
(with Dan Schaal), Adv. in Applied Math 26 (3), 252257.  2000
 1999
 Permutation Patterns and Continued Fractions
(with Herb Wilf and Doron Zeilberger), El. J. of Comb. 6 (1), R38.  Permutations Containing and Avoiding 123 and 132 Patterns
Disc. Math and Theoretical Comp. Sci. 3, 151154.  New Lower Bounds for Some Multicolored Ramsey Numbers
El. J. of Comb. 6 (1), R3.  1998
 1993
Click here for computer programs  teaching

Fall 2017  Spring 2018
I am on leave but around. I will, of course, remain the faculty liaison for Colgate's nationally ranked Women's Ice Hockey team.
 dangerboy

dangerboy is:
An alternative/nerd rock/pop band with 3 members who share one brain.
 aaron plays guitar and sings
 frank plays bass and does backing vocals
 scott plays drums and does backing vocals
 We put the gerbo in dangerboy
some songs
 She Falls Apart (demo)
 Use Me Like You Used The Others (demo)
contact dangerboy
 family

Privacy Policy
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Below are links to all of the computer packages referenced in my papers.
 ZSGS.f and ZSGS2.f: Fortran programs that accompany
Zerosum Generalized Schur Numbers to calculate small examples
and provide maximally valid colors. The files are zipped together.
 ZSAP.f, ZSAP2.f, MZSAP.f, and MZSAP2.f: Fortran programs that accompany
Zerosum Analogues of van der Waerden's Theorem on Arithmetic Progressions to calculate small examples
and provide maximally valid colors. The files are zipped together.
 VOYAGE:
A Maple program that accompanies the paper Rethinking Paleolithic Voyaging. It simulates tsunamis in the Aegean region and accidental crossings on
them as well as population dynamics for said crossers.
 Delaporte Programs:
a zip file for the Python and R scripts used in the article
On the Distribution of Monochromatic Complete Subgraphs and Arithmetic Progressions.
The Python scripts were written by Maria Dascalu and the R scripts
were written by Will Cipolli.
 RADONUMBERS:
a zip file of a C++ program that accompanies
Some Two Color,
Four Variable Rado Numbers.
It was written by Kellen Myers and Joseph Parrish.
It determines, given k and j,
the minimum integer N such that
any 2coloring of [1,N] admits
a monochromatic solution to
x+y+kz=jw.
 FVR:
is a (very short) Maple package that accompanies
Some Two Color,
Four Variable Rado Numbers.
It determines, given a 2coloring, those
values of k for which
x+y+kz=(k+c)w has a monochromatic
solutions (when c is given).
 PABLO:
is a Maple package that accompanies
On the Asymptotic
Minimum Number of Monochromatic 3Term
Arithmetic Progressions.
It verifies the lower bounds given
in the article.
 SCHAAL:
is a Maple package that accompanies
Two Color
Offdiagonal Radotype numbers.
It determines bounds for the
Rado numbers of certain
linear homogeneous equations.
 AB.f:
is a Fortran77 program that accompanies
the article
On the Degree of Regularity of
Generalized van der Waerden Triples
In particular, it proves that the degree
of regularity of (2,2) is
not 1, 2, or infinity.  AARON:
AARON is a Maple package written by Doron
Zeilberger with additions by me. It accompanies
the article
Refined Restricted Permutations.
One use is the enumeration, for small n, of the set of
permutations in S_{n} with
k fixed points which contain
r instances of a given pattern of length 3.
 DIFFSEQ.f:
DIFFSEQ.f is a Fortran program which accompanies the
article Avoiding Monochromatic Sequences
With Special Gaps. It will calculate
f(S,k;2) for many small values of k and
an inputted set S.
 VDW.f:
VDW.f is a Fortran program which accompanies the
article On Generalized
Van der Waerden Triples. It will calculate
N(a,b;2) for many small values of a and b by
a recursive search similar to that used in DF.f.
 AUTOISSAI:
AUTOISSAI is a Maple package which accompanies the
article Offdiagonal
Generalized Schur Numbers. It was used to help
determine the exact values of these numbers, and
is another step towards automated theorem proving.
 MIKLOS:
MIKLOS is a Maple package accompanying the article
Permutation Patterns and Continued Fraction.
It will find, quite quickly thanks to Herb Wilf,
the generating functions for the number of
permutations with either 0 or 1 (132)patterns
and a prescribed number of (123)patterns.
 DF.f,
DF3.f, and
ISSAI: DF.f
(and its 3colored cousin DF3.f) is a Fortran program
which finds the maximal Difference Ramsey number.
ISSAI is a small Maple package for finding lower
bounds and exact values for the newly defined
Issai Numbers, also called Offdiagonal
Generalized Schur Numbers.
These programs accompany the article
Difference Ramsey Numbers and
Issai Numbers.
 RES: RES is a Maple package
accompanying the article New Lower Bounds
for Some Multicolored Ramsey Numbers. By mating the finite
field method of Greenwood and Gleason with today's computing
power, we are able to find good bounds for some large Ramsey numbers.
 RON, GENRON, and SCHUR : RON is a Maple package accompanying the article A 2Coloring of [1,N] Can Have N^2/22 + O(N) Monochromatic Schur Triples, But Not Less!. It will find the number of Schur Triples (asymptotically) of any coloring you enter, along with many other useful tools to attact this problem posed by Ron Graham. GENRON is a Maple package which performs the same tasks as RON, except that we are trying to find the minimum number of monochromatic solutions of x+ay=z (if a=1 then we are counting Schur triples). This extension was posed to me by Ron Graham.
 ZSGS.f and ZSGS2.f: Fortran programs that accompany
Zerosum Generalized Schur Numbers to calculate small examples
and provide maximally valid colors. The files are zipped together.