7 citations · 22 across the 14 of their papers we have counts for
14 papers
The colored edge theory of A. Bulatov and binary absorption in minimal Taylor algebras
Zarathustra Brady, Petar Đapić, Petar Marković +2
We find a new definition of colored edge graphs of finite algebras in the case of minimal Taylor algebras, a definition which includes the graphs invented by A. Bulatov. Next we pr…
On 2-generated minimal Taylor algebras of size 4
Zarathustra Brady, Petar Đapić, Vukašin Đinović +4
We prove that any 2-generated minimal Taylor algebra on a domain of size 4 is not simple. In addition, we find all such algebras up to isomorphism and term-equivalence.
Coarse classification of binary minimal clones
Zarathustra Brady
We classify binary minimal clones into seven categories: affine algebras, rectangular bands, -cyclic groupoids, spirals, non-Taylor partial semilattices, melds, and dispersive a…
Notes on CSPs and Polymorphisms
Zarathustra Brady
These are notes from a multi-year learning seminar on the algebraic approach to Constraint Satisfaction Problems (CSPs). The main topics covered are the theory of algebraic structu…
A Semidefinite Framework for the Sieve
Zarathustra Brady
We describe a semidefinite programming framework for proving upper bounds on concrete sifting problems, and show that the Large Sieve can be interpreted as a special case of this f…
Unifying the Three Algebraic Approaches to the CSP via Minimal Taylor Algebras
Libor Barto, Zarathustra Brady, Andrei Bulatov +2
This paper focuses on the algebraic theory underlying the study of the complexity and the algorithms for the Constraint Satisfaction Problem (CSP). We unify, simplify, and extend p…
Symmetric Operations on Domains of Size at Most 4
Zarathustra Brady, Holden Mui
To convert a fractional solution to an instance of a constraint satisfaction problem into a solution, a rounding scheme is needed, which can be described by a collection of symmetr…
Asymptotics of -Dimensional Visibility
Ezra Erives, Srinivasan Sathiamurthy, Zarathustra Brady
We consider the space , imagined as a three dimensional, axis-aligned grid world partitioned into unit cubes. Each cube is either considered to…
Examples, counterexamples, and structure in bounded width algebras
Zarathustra Brady
We study bounded width algebras which are minimal in the sense that every proper reduct does not have bounded width. We show that minimal bounded width algebras can be arranged int…
A hardness of approximation result in metric geometry
Zarathustra Brady, Larry Guth, Fedor Manin
We show that it is -hard to approximate the hyperspherical radius of a triangulated manifold up to an almost-polynomial factor.
Chromatic numbers of directed hypergraphs with no "bad" cycles
Zarathustra Brady
Imagine that you are handed a rule for determining whether a cycle in a digraph is "good" or "bad", based on which edges of the cycle are traversed in the forward direction and whi…
Sums of seven octahedral numbers
Zarathustra Brady
We show that for a large class of cubic polynomials , every sufficiently large number can be written as a sum of seven positive values of . As a special case, we show that ev…
General divisor function inequalities and the third cumulant
Zarathustra Brady
We extend a lower bound of Munshi on sums over divisors of a number which are less than a fixed power of from the squarefree case to the general case. In the process we pro…
Inequalities and higher order convexity
Zarathustra Brady
We study the following problem: given n real arguments a1, ..., an and n real weights w1, ..., wn, under what conditions does the inequality w1 f(a1) + w2 f(a2) + ... + wn f(an) >=…