3 citations · 3 across the 10 of their papers we have counts for
11 papers
Toric Richardson Varieties and Slice Links
Thomas C. Martinez, Matthew J. Tyler
For type braid varieties, including Richardson varieties and positroid varieties, we prove that the standard torus has a dense orbit exactly when the associated link is smoothl…
The Combinatorics of Affine Deodhar Diagrams
Thomas C. Martinez
Deodhar diagrams give a combinatorial way to compute point counts of open positroid varieties over finite fields. We introduce affine Deodhar diagrams, which extend this constructi…
Unimodality of -Fibonomial coefficients for small cases
Brendan B. Connelly, Ezekiel Ito, Thomas C. Martinez +2
Bergeron--Ceballos--Küstner introduced the -Fibonomial coefficients \( \qfibonom{m+n}{n}\), gave a combinatorial interpretation of the -Fibonomial coefficients via a weighted…
On Benford's Law and the Coefficients of the Riemann Mapping Function for the Exterior of the Mandelbrot Set
Filippo Beretta, Jesse Dimino, Weike Fang +3
We investigate Benford's law in relation to fractal geometry. Basic fractals, such as the Cantor set and Sierpinski triangle are obtained as the limit of iterative sets, and the un…
Class Numbers and Pell's Equation
Thomas Jaklitsch, Thomas C. Martinez, Steven J. Miller +1
Two well-studied Diophantine equations are those of Pythagorean triples and elliptic curves, for the first we have a parametrization through rational points on the unit circle, and…
Connections of Class Numbers to the Group Structure of Generalized Pythagorean Triples
Thomas Jaklitsch, Thomas C. Martinez, Steven J. Miller +1
Two well-studied Diophantine equations are those of Pythagorean triples and elliptic curves; for the first, we have a parametrization through rational points on the unit circle, an…
Generalizing Zeckendorf's Theorem to Homogeneous Linear Recurrences, II
Thomas C. Martinez, Steven J. Miller, Clayton Mizgerd +2
Zeckendorf's theorem states that every positive integer can be written uniquely as the sum of non-consecutive shifted Fibonacci numbers , where we take and …
Counting on Euler and Bernoulli Number Identities
Arthur T. Benjamin, John Lentfer, Thomas C. Martinez
While there are many identities involving the Euler and Bernoulli numbers, they are usually proved analytically or inductively. We prove two identities involving Euler and Bernoull…
On Class Numbers, Torsion Subgroups, and Quadratic Twists of Elliptic Curves
Talia Blum, Caroline Choi, Alexandra Hoey +3
The Mordell-Weil groups of elliptic curves influence the structures of their quadratic twists and the ideal class groups of i…
Generalizing the Distribution of Missing Sums in Sumsets
Hung V. Chu, Dylan King, Noah Luntzlara +5
Given a finite set of integers , its sumset is . We examine as a random variable, where , the set of integer…
Generalizing Zeckendorf's Theorem to Homogeneous Linear Recurrences, I
Thomas C. Martinez, Steven J. Miller, Clayton Mizgerd +1
Zeckendorf's theorem states that every positive integer can be written uniquely as the sum of non-consecutive shifted Fibonacci numbers , where we take and …