Determinant Formulae for some Tiling Problems and Application to Fully Packed Loops

P. Di Francesco ¹, Paul Zinn-Justin ², J. -B. Zuber ²

We present determinant formulae for the number of tilings of various domains in relation with Alternating Sign Matrix and Fully Packed Loop enumeration.

• 1. Service de Physique Théorique (SPhT),
  CNRS : URA2306 – CEA : DSM/SPHT
• 2. Laboratoire de Physique Théorique et Hautes Energies (LPTHE),
  CNRS : UMR7589 – Université Paris VI – Pierre et Marie Curie – Université Paris VII – Paris Diderot