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Atiyah-Singer index theorem
name
Bruck-Ryser-Chowla theorem
name
(mathematics)
A
result
on
the
combinatorics
of
block
designs,
stating
that,
if
a
(v,
b,
r,
k,
λ)-design
exists
with
v
=
b
(a
symmetric
block
design),
then:
(i)
if
v
is
even,
then
k
−
λ
is
a
square;
(ii)
if
v
is
odd,
then
the
following
Diophantine
equation
has
a
nontrivial
solution:
x²
−
(k
−
λ)y²
−
(−1)^((v−1)/2)
λ
z²
=
0.
Bombieri-Friedlander-Iwaniec theorem
name
de Bruijn-Erdős theorem
name
Lefschetz fixed-point theorem
name
Poincaré-Birkhoff-Witt theorem
name
van der Waerden's theorem
name
(mathematics)
In
Ramsey
theory,
a
theorem
stating
that,
for
any
given
positive
integers
r
and
k,
there
is
some
number
N
such
that
if
the
integers
{1,
2,
...,
N}
are
colored,
each
with
one
of
r
different
colors,
then
there
are
at
least
k
integers
in
arithmetic
progression
whose
elements
are
of
the
same
color.
complex conjugate root theorem
name
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