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Crystalline Order in Random Packings of Z-pentominoes on the Square Lattice

March 11, 2026, 12:15 PM - 1:15 PM

Location:

Mathematics Graduate Student Lounge -- 7th Floor

Rutgers University

Hill Center

Mathematics Department

110 Frelinghuysen Road

Piscataway, NJ 08854

Qidong He, Rutgers University

Randomly packed Z-pentominoes on the square lattice are known numerically to undergo a disorder-order phase transition as the packing fraction increases; see the attached images by Barnes (2010). I will prove this by showing that there is order when the packing fraction is sufficiently large, and fully classifying all types of order that can emerge.