[seqfan] Re: Help with A028247 Number of T-frame polyominoes with n cells

[David Radcliffe]

By analogy with the definition of a U-frame, I would guess that a T-frame
is a polyomino whose boundary word has the form

x^a y^b x^c y^d x^-e y^-f x^g y^-h

where a, b, c, d, e, f, g, h are positive integers.

The boundary word is determined by moving counterclockwise around the
boundary of the polyomino. The symbols x and y represent unit steps to the
right and up, respectively, while x^-1 and y^-1 represent steps to the left
and down.

Note that the T-tetronimo has boundary word xyxyx^-3y^-1xy^-1, so my
proposed definition of T-frame is an obvious generalization.

I found 6 distinct T-frame hexominoes. I have attached an image if that is
allowed. Otherwise, here is a text version:

XXXXX
..X..

XXXXX
.X...

XXXX
.X..
.X..

X...
XXXX
X...

XXXX
.XX.

XXX
XX.
.X

There is an online book on Polyominoes
<http://code-spot.co.za/downloads/polyominoes/Polyominoes.pdf> which has
more information about polyominoes, including discussion of boundary words
and U-frames.

On Tue, Jan 31, 2023 at 10:13 AM Michel Marcus <michel.marcus183 at gmail.com>
wrote:

> There are U-frames in https://doi.org/10.1016/0097-3165(91)90013-7.
> Best .
> MM
>
> Le mar. 31 janv. 2023 à 16:12, John Mason <masonmilan33 at gmail.com> a
> écrit :
>
> > Hi sequence fans
> > Does anyone know what a T-frame polyomino is?
> > I tried writing to the email address given in the sequence but to no
> avail.
> > I tried identifying polyominoes that look like a T but for a(6) I found
> > only 5.
> > Any ideas?
> > Thanks
> > john
> >
> > --
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> >
>
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