Joshua Brakensiek

activity

20132026

most citedEfficient Geometric Probabilities of Multi-Transiting Exoplanetary Systems from CORBITS

48 citations · 103 across the 33 of their papers we have counts for

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4 papers · 1 filter

math.CO2026

Multiplicative error set system sparsification: A simpler proof via chain length contraction

Joshua Brakensiek, Venkatesan Guruswami, Aaron Putterman

The chain length of a set family $S \subseteq 2^{[m]}$ is the largest ascending sequence of sets in containment order in the union-closure of $S$ . In this work,…

math.CO2024

Rigidity matroids and linear algebraic matroids with applications to matrix completion and tensor codes

Joshua Brakensiek, Manik Dhar, Jiyang Gao +2

We establish a connection between problems studied in rigidity theory and matroids arising from linear algebraic constructions like tensor products and symmetric products. A specia…

math.CO2019

The Resolution of Keller's Conjecture

Joshua Brakensiek, Marijn Heule, John Mackey +1

We consider three graphs, $G_{7, 3}$ , $G_{7, 4}$ , and $G_{7, 6}$ , related to Keller's conjecture in dimension 7. The conjecture is false for this dimension if and only if at least one…

math.CO2017

Vertex isoperimetry and independent set stability for tensor powers of cliques

Joshua Brakensiek

The tensor power of the clique on $t$ vertices (denoted by $K_{t}^{n}$ ) is the graph on vertex set ${1, ..., t}^{n}$ such that two vertices $x, y \in {1, ..., t}^{n}$ are connected if…