Anzeige
Erschienen in:
2011 | OriginalPaper | Buchkapitel
Enumerating Tatami Mat Arrangements of Square Grids
verfasst von : Alejandro Erickson, Mark Schurch
Erschienen in: Combinatorial Algorithms
Verlag: Springer Berlin Heidelberg
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
We prove that the number of monomer-dimer tilings of an
n
×
n
square grid, with
m
<
n
monomers in which no four tiles meet at any point is
m
2
m
+ (
m
+ 1)2
m
+ 1
, when
m
and
n
have the same parity. In addition, we present a new proof of the result that there are
n
2
n
− 1
such tilings with
n
monomers, which divides the tilings into
n
classes of size 2
n
− 1
. The sum of these over all
m
≤
n
has the closed form 2
n
− 1
(3
n
− 4) + 2 and, curiously, this is equal to the sum of the squares of all parts in all compositions of
n
.