4 citations · 22 across the 26 of their papers we have counts for
28 papers
Big Ramsey Degrees of Countable Ordinals
Joanna Boyland, William Gasarch, Nathan Hurtig +1
Ramsey's theorem states that for all finite colorings of an infinite set, there exists an infinite homogeneous subset. What if we seek a homogeneous subset that is also order-equiv…
Fermat's Last Theorem, Schur's Theorem (in Ramsey Theory), and the Infinitude of the Primes
William Gasarch
Alpoge and Granville (separately) gave novel proofs that the primes are infinite that use Ramsey Theory. In particular, they use Van der Waerden's Theorem and some number theory. W…
Alternative Paradigms of Computation
William Gasarch, Nathan Hayes, Emily Kaplitz +1
With Moore's law coming to a close it is useful to look at other forms of computer hardware. In this paper we survey what is known about several modes of computation: Neuromorphic,…
An Empirical Comparison of the Quadratic Sieve Factoring Algorithm and the Pollard Rho Factoring Algorithm
Zongxia Li, William Gasarch
One of the most significant challenges on cryptography today is the problem of factoring large integers since there are no algorithms that can factor in polynomial time, and factor…
Hilbert's Tenth Problem: Refinements and Variants
William Gasarch
Hilbert's 10th problem, stated in modern terms, is: Find an algorithm that will, given determine if there exists $a_1, a_2, \ldots, a_n \in \math…
NIM with Cash: A Concrete Approach
Douglas Chen, William Gasarch
Let A be a finite subset of the naturals and let n be a natural. Let NIM(A;n) be the two player game in which players alternate removing stones from a pile with stones…