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Enumeration of symmetry classes of convex polyominoes on the honeycomb lattice

Article by Gouyou-Beauchamps, Dominique and Leroux, Pierre
  • Published in 2005
  • Added on
We enumerate the symmetry classes of convex polyominoes on the hexagonal (honeycomb) lattice. Here convexity is to be understood as convexity along the three main column directions. We deduce the generating series of free (i.e. up to reflection and rotation) and of asymmetric convex hexagonal polyominoes, according to area and half-perimeter. We give explicit formulas or implicit functional equations for the generating series, which are convenient for computer algebra. Thus, computations can be carried out up to area 70.

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Other information

issn
03043975
journal
Theoretical Computer Science
number
2-3
pages
307--334
volume
346

BibTeX entry

@article{Gouyou-Beauchamps2005,
	abstract = {We enumerate the symmetry classes of convex polyominoes on the hexagonal (honeycomb) lattice. Here convexity is to be understood as convexity along the three main column directions. We deduce the generating series of free (i.e. up to reflection and rotation) and of asymmetric convex hexagonal polyominoes, according to area and half-perimeter. We give explicit formulas or implicit functional equations for the generating series, which are convenient for computer algebra. Thus, computations can be carried out up to area 70.},
	author = {Gouyou-Beauchamps, Dominique and Leroux, Pierre},
	issn = 03043975,
	journal = {Theoretical Computer Science},
	month = {nov},
	number = {2-3},
	pages = {307--334},
	title = {Enumeration of symmetry classes of convex polyominoes on the honeycomb lattice},
	url = {http://www.sciencedirect.com/science/article/pii/S0304397505004950},
	volume = 346,
	year = 2005,
	urldate = {2015-02-02}
}