Editing Polyomino (section)

===Special classes of polyominoes===
Exact formulas are known for enumerating polyominoes of special classes, such as the class of ''convex'' polyominoes and the class of ''directed'' polyominoes.

The definition of a ''convex'' polyomino is different from the usual definition of [[Convex set|convexity]], but is similar to the definition used for the [[orthogonal convex hull]]. A polyomino is said to be ''vertically'' or ''column convex'' if its intersection with any vertical line is convex (in other words, each column has no holes). Similarly, a polyomino is said to be ''horizontally'' or ''row convex'' if its intersection with any horizontal line is convex.  A polyomino is said to be ''convex'' if it is row and column convex.<ref name=W151>{{cite book | last=Wilf | first=Herbert S. | author-link=Herbert Wilf | title=Generatingfunctionology | edition=2nd | location=Boston, MA | publisher=Academic Press | year=1994 | isbn=978-0-12-751956-2 | zbl=0831.05001 | page=151 }}</ref>

A polyomino is said to be ''directed'' if it contains a square, known as the ''root'', such that every other square can be reached by movements of up or right one square, without leaving the polyomino.

Directed polyominoes,<ref>{{cite journal |last=Bousquet-Mélou |first=Mireille | author-link = Mireille Bousquet-Mélou |year=1998 |title=New enumerative results on two-dimensional directed animals |journal=Discrete Mathematics |volume=180 |issue=1–3 |pages=73–106 |doi=10.1016/S0012-365X(97)00109-X|doi-access=free }}</ref> column (or row) convex polyominoes,<ref>{{cite journal |last=Delest |first=M.-P. |year=1988 |title=Generating functions for column-convex polyominoes |journal=Journal of Combinatorial Theory, Series A |volume=48 |issue=1 |pages=12–31 |doi=10.1016/0097-3165(88)90071-4|doi-access=free }}</ref> and convex polyominoes<ref>{{cite journal |last1=Bousquet-Mélou |first1=Mireille | author1-link = Mireille Bousquet-Mélou |last2=Fédou | first2 = Jean-Marc |year=1995 |title=The generating function of convex polyominoes: The resolution of a ''q''-differential system |journal=[[Discrete Mathematics (journal)|Discrete Mathematics]] |volume=137 |issue=1–3 |pages=53–75 |doi=10.1016/0012-365X(93)E0161-V|doi-access=free }}</ref> have been effectively enumerated by area ''n'', as well as by some other parameters such as perimeter, using [[generating function]]s.

A polyomino is [[equable shape|equable]] if its area equals its perimeter. An equable polyomino must be made from an [[even number]] of squares; every even number greater than 15 is possible. For instance, the 16-omino in the form of a 4&nbsp;&times;&nbsp;4 square and the 18-omino in the form of a 3&nbsp;&times;&nbsp;6 rectangle are both equable. For polyominoes with 15 squares or fewer, the perimeter always exceeds the area.<ref>{{citation|title=Geometry Labs|first=Henri|last=Picciotto|year=1999|publisher=MathEducationPage.org|page=208|url=https://books.google.com/books?id=7gTMKr7TT6gC&pg=PA208}}.</ref>