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Kellen Myers - Homepage

Office: Whitman 180 K [map ],
Office Hours: Wednesdays 1:30-4:30 (open), Thursdays 2:00-3:00 (open), and Tuesdays 2:00-3:00 by appointment,
Email: kellen.myers [at] farmingdale [dot] edu, for teaching and Farmingdale matters,
Email: kellen.myers [at] gmail [dot] com, for research and other matters

Welcome to my homepage. I am an Assistant Professor in the Department of Mathematics at Farmingdale State College (SUNY Farmingdale) . I completed my PhD in Mathematics at Rutgers University where my advisor was Doron Zeilberger . I hope you enjoy my website.

Kellen Myers & Aaron Robertson, Two Color Off-Diagonal Rado-Type Numbers, Electronic Journal of Combinatorics, 14(1), R53.
[abstract] [PDF file] [arXiv preprint] [El. J. Comb. journal] [Aaron Robertson person]

My research interests are in combinatorics. The problems I work on are in the area of Ramsey theory, in particular Diophantine Ramsey theory, the study of the Ramsey-theoretic properties of the integer solutions to equations. My research focuses on computer-diven methods. I am also interested in analytical methods in Diophantine Ramsey theory, which really means number theory and additive combinatorics, but from a non-typical point-of-view.

I also enjoy problems and methods from other areas, like set systems or game theory. I would characterize my interest in mathematics, in general, as very broad. I enjoy the interdisciplinary nature of mathematics and appreciate collaboration between mathematicians with diverse interests, and between mathematicians and people in other areas of scholarship. I am also a proponent of computer-based pedagogy and active learning in the mathematics classroom. Lastly, my Erdős number is 3 (check here ).

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Kellen Myers & Aaron Robertson, Two Color Off-Diagonal Rado-Type Numbers, Abstract:

We show that for any two linear homogeneous equations E0, E1, each with at least three variables and coefficients not all the same sign, any 2-coloring of Z+ admits monochromatic solutions of color 0 to E0 or monochromatic solutions of color 1 to E1. We define the 2-color off-diagonal Rado number RR(E0; E1) to be the smallest N such that [1,N] must admit such solutions. We determine a lower bound for RR(E0, E1) in certain cases when each Ei is of the form a1x1 + ... + anxn = z as well as find the exact value of RR(E0, E1) when each is of the form x1 + a2x2 + ... + anxn = z. We then present a Maple package that determines upper bounds for off-diagonal Rado numbers of a few particular types, and use it to quickly prove two previous results for diagonal Rado numbers.

Kellen Myers & Aaron Robertson, Two Color Off-Diagonal Rado-Type Numbers, Abstract:

There exists a minimum integer N such that any 2-coloring of {1, 2, ... , N} admits a monochromatic solution to x+y+kz = lw for k,l in Z+, where N depends on k and l. We determine N when l-k is in {0, 1, 2, 3, 4, 5}, and for all k, l for which (1/2)((l-k)2 -2)(l-k+1) ≤ k ≤ l - 4, as well as for arbitrary k when l = 2.

K. Myers → A. Robertson → T. C. Brown → P. Erdős