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Showing 2026 · math.COShow all
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math.CO2026
The satisfiability threshold of random linear equations over finite commutative rings
Pu Gao, Theodore Morrison
We extend the study of random linear equations over finite fields to equations over finite commutative rings. We characterize precisely when the satisfiability threshold occurs at…
math.CO2026
When are random regular triangle-free graphs bipartite?
Gregory DeCamillis, Pu Gao
We study the structure of random -regular triangle-free graphs and show that a sharp phase transition occurs at . For smaller , asymptotic…
math.CO2026
Non-uniform Kahn-Kalai, spread, variants, and applications
Thinula De Silva, Pu Gao
Building on B.Park and Vondrak's recent generalization of the J.Park-Pham Theorem (formerly known as Kahn-Kalai conjecture) to non-uniform probability measures, this paper introduc…