3 papers
cs.CC2026
Spiky Rank and Its Applications to Rigidity and Circuits
Lianna Hambardzumyan, Konstantin Myasnikov, Artur Riazanov +2
We introduce spiky rank, a new matrix parameter that enhances blocky rank by combining the combinatorial structure of the latter with linear-algebraic flexibility. A spiky matrix i…
cs.CC2026
The Log-Rank Conjecture: New Equivalent Formulations
Lianna Hambardzumyan, Shachar Lovett, Morgan Shirley
The log-rank conjecture is a longstanding open problem with multiple equivalent formulations in complexity theory and mathematics. In its linear-algebraic form, it asserts that the…
math.CO2025
Factorization norms and an inverse theorem for MaxCut
Igor Balla, Lianna Hambardzumyan, István Tomon
We prove that Boolean matrices with bounded -norm or bounded normalized trace norm must contain a linear-sized all-ones or all-zeros submatrix, verifying a conjecture of Hamb…