I have been very intrigued by the theory of arithmetic combinatorics after the result regarding primes in arithmetic progressions proven by Tao and Green. PAPERS ARE OK. I notice that most people usually skip out on papers, but papers are what got me into the theory. I have found a book, (additive combinatorics-Tao), which so far seems quite nice. But for instance, are there any notes, or "paper-notes" or EVEN lectures based around, or even on this topic? Even some other books talking about this theory, or things related to that? (I have watched the Ben Green lectures on higher-order Fourier analysis, and I am aware of Tao's notes on this subject).
2026-02-23 12:49:53.1771850993
What are some good resources to learn arithmetic combinatorics?
215 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in COMBINATORICS
- Using only the digits 2,3,9, how many six-digit numbers can be formed which are divisible by 6?
- The function $f(x)=$ ${b^mx^m}\over(1-bx)^{m+1}$ is a generating function of the sequence $\{a_n\}$. Find the coefficient of $x^n$
- Name of Theorem for Coloring of $\{1, \dots, n\}$
- Hard combinatorial identity: $\sum_{l=0}^p(-1)^l\binom{2l}{l}\binom{k}{p-l}\binom{2k+2l-2p}{k+l-p}^{-1}=4^p\binom{k-1}{p}\binom{2k}{k}^{-1}$
- Algebraic step including finite sum and binomial coefficient
- nth letter of lexicographically ordered substrings
- Count of possible money splits
- Covering vector space over finite field by subspaces
- A certain partition of 28
- Counting argument proof or inductive proof of $F_1 {n \choose1}+...+F_n {n \choose n} = F_{2n}$ where $F_i$ are Fibonacci
Related Questions in ARITHMETIC
- Solve this arithmetic question without algebra
- Is division inherently the last operation when using fraction notation or is the order of operation always PEMDAS?
- Upper bound for recursion?
- Proving in different ways that $n^{n-1}-1$ is divisible by $(n-1)^2$.
- Meaning of a percentage of something
- Compare $2^{2016}$ and $10^{605}$ without a calculator
- The older you are, the richer you get?
- Easy question which doesn't make sense to me!
- Calculating diminishing interest amount
- Multiplication Question
Related Questions in ARITHMETIC-PROGRESSIONS
- How to solve a quartic equation given that the roots are all part of an arithmetic sequence?
- Defining a rigorous equation for the distance
- How do I solve the following exercise?
- Upper bound for recursion?
- $a, 1, b$ are three consecutive terms of an arithmetic series, find $a, b$ and $S$ of the infinite geometric series
- I am stuck on a question Algebra:Sequence and series, Can we make an infinitely long arithmetic progression from the set of prime integers?
- General formula for natural power summation
- How do I proceed with this?
- Find the total number of identical terms in 2 sequences.
- Is there generalization for gamma function?
Related Questions in ADDITIVE-COMBINATORICS
- Exercise 1.1.6 in Additive Combinatorics
- Show that $A+B$ contains at least $m+n-1$ elements.
- Advantage of Fourier transform on $\mathbb{Z}_N$
- Sorting on non-additive ratios
- Asymptotic formula for the integral sequence s(n)
- Show that $|A+A| < 2.5 |A| $ with $A = \{ [n \sqrt{2}] : 1 \leq n \leq N \}$
- show that $[n \sqrt{3}]$ is an approximate group
- A combinatoric solution (closed expression) for $\sum_{k=i}^n \binom{n}{k}p^k(1-p)^{n-k}$
- On Gowers' approach of Green-Tao Theorem ($\mathcal{D}f$s span $L^q(\mathbb{Z}_N)$).
- Is that specific function additive under disjoint union?
Related Questions in ARITHMETIC-COMBINATORICS
- Minors of a particular matrix?
- Erdos conjecture on arithmetic progression
- Parity of Partition Function
- Efficient way to count number of arithmetic progression on coloring of $\mathbb{N}$.
- How prove that there are $a,b,c$ such that $a \in A, b \in B, c \in C$ and $a,b,c$ (with approriate order) is a arithmetic sequence?
- Circular variation with repetition
- Number of sudokus with no consecutive arithmetic progression of length 3 in any row or column.
- this is a conjecture or a result? every arithmetic progression contains a sequence of $k$ "consecutive" primes for possibly all natural numbers $k$?
- Arithmetic Progressions in slowly oscillating sequences
- Boundedness of $\gcd(|x-y|,|a_x-a_y|)$ in sequence
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
By no means am I an expert on this, so I don't know how good these resources are. However, these are other resources you might find helpful:
Additive Combinatorics is also known as Discrete Harmonic Analysis in some circles (no pun intended). There is a book on Discrete Harmonic Analysis here:
If you are interested in a Theoretical Computer Science perspective, there are a couple good starting points:
I hope this is helpful!