Tiling generating functions of halved hexagons and quartered hexagons

Abstract

We prove exact product formulas for the tiling generating functions of various halved hexagons and quartered hexagons with defects on boundary. Our results generalize the previous work of the first author and the work of Ciucu.

30 pages. V2: Fixed typos in Theorem 2.2 and Theorem 2.4

References in corpus (2)

• Bijective proofs of skew Schur polynomial factorizations
• A Shuffling Theorem for Reflectively Symmetric Tilings

Cited by in corpus (2)

• Tilted Halved Hexagons: Hexagons, Semi-hexagons, and Halved Hexagons Under One Roof
• The generating function of lozenge tilings for a "quarter" of a hexagon, obtained with non--intersecting lattice paths