Doubling and difference constants #
This file defines the doubling and difference constants of two finsets in a group.
The doubling constant σ[A, B]
of two finsets A
and B
in a group is |A + B| / |A|
.
The notation σ[A, B]
is available in scope Combinatorics.Additive
.
Instances For
The doubling constant σₘ[A, B]
of two finsets A
and B
in a group is |A * B| / |A|
.
The notation σₘ[A, B]
is available in scope Combinatorics.Additive
.
Instances For
The difference constant σ[A, B]
of two finsets A
and B
in a group is |A - B| / |A|
.
The notation δ[A, B]
is available in scope Combinatorics.Additive
.
Instances For
The difference constant δₘ[A, B]
of two finsets A
and B
in a group is |A / B| / |A|
.
The notation δₘ[A, B]
is available in scope Combinatorics.Additive
.
Instances For
The doubling constant σₘ[A, B]
of two finsets A
and B
in a group is |A * B| / |A|
.
Equations
- One or more equations did not get rendered due to their size.
Instances For
Pretty printer defined by notation3
command.
Equations
- One or more equations did not get rendered due to their size.
Instances For
The doubling constant σₘ[A]
of a finset A
in a group is |A * A| / |A|
.
Equations
- One or more equations did not get rendered due to their size.
Instances For
Pretty printer defined by notation3
command.
Equations
- One or more equations did not get rendered due to their size.
Instances For
The doubling constant σ[A, B]
of two finsets A
and B
in a group is |A + B| / |A|
.
Equations
- One or more equations did not get rendered due to their size.
Instances For
Pretty printer defined by notation3
command.
Equations
- One or more equations did not get rendered due to their size.
Instances For
The doubling constant σ[A]
of a finset A
in a group is |A + A| / |A|
.
Equations
- One or more equations did not get rendered due to their size.
Instances For
Pretty printer defined by notation3
command.
Equations
- One or more equations did not get rendered due to their size.
Instances For
The difference constant σₘ[A, B]
of two finsets A
and B
in a group is |A / B| / |A|
.
Equations
- One or more equations did not get rendered due to their size.
Instances For
Pretty printer defined by notation3
command.
Equations
- One or more equations did not get rendered due to their size.
Instances For
The difference constant σₘ[A]
of a finset A
in a group is |A / A| / |A|
.
Equations
- One or more equations did not get rendered due to their size.
Instances For
Pretty printer defined by notation3
command.
Equations
- One or more equations did not get rendered due to their size.
Instances For
The difference constant σ[A, B]
of two finsets A
and B
in a group is |A - B| / |A|
.
Equations
- One or more equations did not get rendered due to their size.
Instances For
Pretty printer defined by notation3
command.
Equations
- One or more equations did not get rendered due to their size.
Instances For
Pretty printer defined by notation3
command.
Equations
- One or more equations did not get rendered due to their size.
Instances For
The difference constant σ[A]
of a finset A
in a group is |A - A| / |A|
.
Equations
- One or more equations did not get rendered due to their size.
Instances For
Dense sets have small doubling.
Dense sets have small doubling.
Dense sets have small difference constant.
Dense sets have small difference constant.
If A
has small difference, then it has small doubling, with the constant squared.
This is a consequence of the Ruzsa triangle inequality.
If A
has small difference, then it has small doubling, with the constant squared.
This is a consequence of the Ruzsa triangle inequality.
If A
has small doubling, then it has small difference, with the constant squared.
This is a consequence of the Ruzsa triangle inequality.
If A
has small doubling, then it has small difference, with the constant squared.
This is a consequence of the Ruzsa triangle inequality.