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Ferrers

Ferrers is a naming convention used in combinatorial mathematics, specifically in the study of partitions of integers. It is named after Norman Macleod Ferrers, an Anglo-Scottish mathematician who first introduced it in the 19th century.

A Ferrers diagram, also known as a partition diagram or a Young diagram, is a graphical representation

Ferrers diagrams are used to study various properties of integer partitions, such as their generating functions

The Ferrers naming convention is often used to describe a partition's shape, which is the number of

of
an
integer
partition.
The
diagram
consists
of
a
set
of
left-aligned
rows
of
dots,
where
each
row
has
fewer
dots
than
the
row
above
it.
The
number
of
dots
in
each
row
corresponds
to
the
size
of
each
part
in
the
partition.
For
example,
a
Ferrers
diagram
representing
the
partition
5
+
4
+
2
+
1
would
have
five
dots
in
the
first
row,
four
dots
in
the
second
row,
two
dots
in
the
third
row,
and
one
dot
in
the
fourth
row.
and
hook
lengths.
They
are
also
employed
in
the
theory
of
Young
tableaux,
which
is
a
type
of
combinatorial
object
that
arises
in
representation
theory.
Ferrers
diagrams
have
applications
in
a
wide
range
of
areas,
including
algebraic
combinatorics,
mathematical
physics,
and
computer
science.
rows
or
columns
in
the
diagram.
The
Ferrers
shape
of
a
partition
can
be
rectangular,
square,
or
exceptionally
shaped,
depending
on
the
specific
structure
of
the
partition.
The
study
of
Ferrers
diagrams
has
contributed
significantly
to
our
understanding
of
the
underlying
structure
of
integer
partitions
and
their
applications
in
various
fields
of
mathematics.