3 papers
cs.CC2025
Tensor decomposition beyond uniqueness, with an application to the minrank problem
Pascal Koiran, Rafael Oliveira
We prove a generalization to Jennrich's uniqueness theorem for tensor decompositions in the undercomplete setting. Our uniqueness theorem is based on an alternative definition of t…
cs.CC2025
Rank Bounds and PIT for circuits via a non-linear Edelstein-Kelly theorem
Abhibhav Garg, Rafael Oliveira, Akash Kumar Sengupta
We prove a non-linear Edelstein-Kelly theorem for polynomials of constant degree, fully settling a stronger form of Conjecture 30 in Gupta (2014), and generalizing the main result…
cs.CC2025
Primes via Zeros: Interactive Proofs for Testing Primality of Natural Classes of Ideals
Abhibhav Garg, Rafael Oliveira, Nitin Saxena
A central question in mathematics and computer science is the question of determining whether a given ideal is prime, which geometrically corresponds to the zero set of , de…