In what situations, if any, do Diophantine approximations of numbers come up when attempting to count something? In other words, what are some combinatorics applications of Diophantine approximations that arise from "natural problems"/easy-to-explain problems?
2026-03-25 19:59:03.1774468743
Applications of diophantine approximation in counting (combinatorics).
30 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated 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 BIG-LIST
- Good ideas for communicating the joy of mathematics to nine and ten year olds
- Has miscommunication ever benefited mathematics? Let's list examples.
- What are some great examples of cooperative games with stochastic payoffs?
- Nowhere-differentiable Lipschitz-continuous function
- Ill-known/original/interesting investigations on/applications of inversion (the geometric transform)
- What infinite prime products have $\zeta$-regularized values?
- Mathematical ideas that took long to define rigorously
- Conjectures Disproven by the use of Computers?
- What's new in higher dimensions?
- Math Examples to get High-Schoolers Interested
Related Questions in DIOPHANTINE-APPROXIMATION
- Find $\frac{a}{b} \in \mathbb{Q}$ such that $ |\,\frac{a}{b} - \sqrt{2}|_3 < \epsilon $
- Real part of complex root of $X^5-X-k^5+k+1$ is $\frac{1}{23k}$ away from any integer ($k\geq 2$)
- Fractional part of rational powers
- Dirichlet's approximation theorem
- Can interesting bounds to Gauss circle problem be seen/come from counting points close to a line?
- Lagrange spectrum in diophantine approximation theory
- Dirichlet's Approximation Theorem for integer
- Diophantine condition of irrational numbers
- Continued fraction rate of convergence
- Determine all limits of subsequences of $|\lambda \alpha^n +\mu \bar{\alpha}^n|$ (assume $|\alpha|>1$)
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?