Séminaire Lotharingien de Combinatoire, 95B.104 (2026), 12 pp.
Takashi Imamura, Matteo Mucciconi, Tomohiro Sasamoto and Travis Scrimshaw
The Periodic Multi-Layer Polynuclear Growth: Integrability and Applications
Abstract.
We introduce the periodic multi-layer polynuclear growth dynamics, a
deterministic evolution of sequences of height function
(hi(x,t))i ∈ Z,
where x ∈ R/Z and t ∈ R is the time. This dynamics is integrable: it possesses solitionic behavior, it has a rich set of symmetries and can be reduced, through a projection to the box-ball system (BBS). The inverse scattering map is a generalization of Kerov-Kirillov-Reshetikhin, which linearizes the BBS dynamics. The action of the inverse scattering map on special classes of initial data yields bijective proofs of summation identities for transformed Hall-Littlewood polynomials. These have applications in the description of height distribution of growth processes.
Received: November 15, 2025.
Accepted: February 15, 2026.
Final version: April 1, 2026.
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