4 citations · 11 across the 8 of their papers we have counts for
10 papers
Regarding two conjectures on clique and biclique partitions
Dhruv Rohatgi, John C. Urschel, Jake Wellens
For a graph , let denote the minimum number of cliques of needed to cover the edges of exactly once. Similarly, let denote the minimum number of bicliq…
Relationships between the number of inputs and other complexity measures of Boolean functions
Jake Wellens
We generalize and extend the ideas in a recent paper of Chiarelli, Hatami and Saks to prove new bounds on the number of relevant variables for boolean functions in terms of a varie…
Testing Gap k-planarity is NP-complete
John C. Urschel, Jake Wellens
For all , we show that deciding whether a graph is -planar is NP-complete, extending the well-known fact that deciding 1-planarity is NP-complete. Furthermore, we show…
A tighter bound on the number of relevant variables in a bounded degree Boolean function
Jake Wellens
A classical theorem of Nisan and Szegedy says that a boolean function with degree as a real polynomial depends on at most of its variables. In recent work by Chiarel…
A note on partial rejection sampling for the hard disks model in the plane
Jake Wellens
In this note, we slightly improve the guarantees obtained by Guo and Jerrum for sampling from the hard disks model in the plane via partial rejection sampling. Our proof makes use…
On Graphs and the Gotsman-Linial Conjecture for d = 2
Hyo Won Kim, Chris Maldonado, Jake Wellens
We give an infinite class of counterexamples to the Gotsman-Linial conjecture when d = 2. On the other hand, we establish an asymptotic form of the conjecture for quadratic thresho…
Subcritical behavior for quasi-periodic Schrödinger cocycles with trigonometric potentials
C. A. Marx, L. H. Shou, J. L. Wellens
We give a criterion implying subcritical behavior for quasi-periodic Schrödinger operators where the potential sampling function is given by a trigonometric polynomial. Subcritical…
Sets Characterized by Missing Sums and Differences in Dilating Polytopes
Thao Do, Archit Kulkarni, Steven J. Miller +3
A sum-dominant set is a finite set of integers such that . As a typical pair of elements contributes one sum and two differences, we expect sum-dominant sets to…
Continued fraction digit averages an Maclaurin's inequalities
Francesco Cellarosi, Doug Hensley, Steven J. Miller +1
A classical result of Khinchin says that for almost all real numbers , the geometric mean of the first digits in the continued fraction expansion of converges t…
Sums and differences of correlated random sets
Thao Do, Archit Kulkarni, Steven J. Miller +2
Many fundamental questions in additive number theory (such as Goldbach's conjecture, Fermat's last theorem, and the Twin Primes conjecture) can be expressed in the language of sum…