How many ways can you paint a regular Decagon with q colors?
I need to solve it with Burnside's lemma.
So far I managed to find only 2 symmetries, the identity, and this one.
I believe I miss the method, can someone solve, and try to explain how did he solve it?
2026-03-27 15:36:05.1774625765
How many ways can you paint a regular Decagon with q colors? Solve with Burnside's lemma
108 Views Asked by user876707 https://math.techqa.club/user/user876707/detail AtRelated Questions in GROUP-THEORY
- What is the intersection of the vertices of a face of a simplicial complex?
- Group with order $pq$ has subgroups of order $p$ and $q$
- How to construct a group whose "size" grows between polynomially and exponentially.
- Conjugacy class formula
- $G$ abelian when $Z(G)$ is a proper subset of $G$?
- A group of order 189 is not simple
- Minimal dimension needed for linearization of group action
- For a $G$ a finite subgroup of $\mathbb{GL}_2(\mathbb{R})$ of rank $3$, show that $f^2 = \textrm{Id}$ for all $f \in G$
- subgroups that contain a normal subgroup is also normal
- Could anyone give an **example** that a problem that can be solved by creating a new group?
Related Questions in COLORING
- Name of Theorem for Coloring of $\{1, \dots, n\}$
- Is it true that if a graph is bipartite iff it is class 1 (edge-coloring)?
- Orbit counting lemma hexagon
- difference between colouring number and chromatic number
- Is it a tetrahedron, 5-cell, or something else?
- Distance of closest neighbor points in a vectorspace ${\mathbb R}^n$ (infinitesimal or zero)?
- How to uniquely label a connected graph?
- Graph coloring: $G$ is a graph where the number of vertices with degree of at least $k$, is at most $k$. Prove $χ(G) \le k$
- Complete graphs in the plane with colored edges where an edge don't cross edges with same color
- 4-chromatic unit distance graph with no 4-cycles.
Related Questions in SYMMETRY
- Do projective transforms preserve circle centres?
- Decomposing an arbitrary rank tensor into components with symmetries
- A closed manifold of negative Ricci curvature has no conformal vector fields
- Show, by means of an example, that the group of symmetries of a subset X of a Euclidean space is, in general, smaller than Sym(x).
- How many solutions are there if you draw 14 Crosses in a 6x6 Grid?
- Symmetry of the tetrahedron as a subgroup of the cube
- Number of unique integer coordinate points in an $n$- dimensional hyperbolic-edged tetrahedron
- The stretch factors of $A^T A$ are the eigenvalues of $A^T A$
- The square root of a positive semidefinite matrix
- Every conformal vector field on $\mathbb{R}^n$ is homothetic?
Related Questions in FIXED-POINTS
- Banach and Caristi fixed point theorems
- Using Fixed point iteration to find sum of a Serias
- Do chaos and/or limit cycles always require the existence of an unstable fixed point?
- Dynamical System is fixed point at origin hyperbolic or asymptotically stable and is the system Hamiltonian
- What type of bifurcation point is this?
- Finding an eigenvector (fixed point) of a linear system of equations
- Only closed homoclinic orbits?
- Is this mapping contractive?
- Fixed points of absolute set difference
- Convergence rate of Newton's method (Modified+Linear)
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?