# L

## Latin Square

A Latin Square of order n is an nxn array made from the integers 1 to n with
the property that any integer occurs once in each row and column.

A pair of Latin squares are called orthogonal if the n-squared pairs formed
by juxtaposing the two arrays are all distinct.

## Lattice (def. 1)

A subset of real or complex (or quaternionic)
*n*-space that consists of all finite sums of a set of
*n* independent generating vectors
with coefficients in the corresponding ring
of integers.

## Lattice (def. 2)

An algebraic system generalizing the notion
of unions and intersections of sets.

## Laminated Lattice

A lattice (in the sense of def. 1) that is built up in layers. One takes an *n*-dimensional
lattice,
and in *n+1*-dimensional space place copies of it next to one
another so as to build up an *n+1*-dimensional lattice. The vectors
that determine how succeeding layers lie next to one another are called
"glue vectors".

The lattice that is used to store cannonballs, (and to display fruit) is
a laminated lattice built up out of successive layers of the hexagonal
close packing.

A -
B -
C -
D -
E -
F -
G -
H -
I -
J -
K -
L -
M -
N -
O -
P -
Q -
R -
S -
T -
U -
V -
W -
X -
Y -
Z

An On-line Dictionary of Combinatorics