Enumeration of various animals on the triangular lattice
نویسندگان
چکیده
In this paper, we consider various classes of polyiamonds that are animals residing on the triangular lattice. By careful analyses through certain layer-by-layer decompositions and cell pruning/growing arguments, derive explicit forms for generating functions number nonempty translation-invariant baryiamonds (bargraphs in lattice), column-convex polyiamonds, convex with respect to their perimeter. particular, show (A) perimeter n asymptotically (?+1)2?4+?3?2?+12?n3??n?2,where ? is a root polynomial degree 5. (B) asymptotic (1799780917+33?13?175463)9517?11927?432?8926?n33+172n?1. (C) 12804413?n33n.
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2021
ISSN: ['1095-9971', '0195-6698']
DOI: https://doi.org/10.1016/j.ejc.2020.103294