I came up with the following:
I don't know if I have proven this appropriately. A friend of mine told me I had to match C with D and from there prove that there is a blocking pair. I'm not sure which way is the correct way.
2026-03-27 02:37:25.1774579045
proof that a stable matching in the roommate's problem is not guaranteed when there are even numbers
528 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in ALGORITHMS
- Least Absolute Deviation (LAD) Line Fitting / Regression
- Do these special substring sets form a matroid?
- Modified conjugate gradient method to minimise quadratic functional restricted to positive solutions
- Correct way to prove Big O statement
- Product of sums of all subsets mod $k$?
- (logn)^(logn) = n^(log10+logn). WHY?
- Clarificaiton on barycentric coordinates
- Minimum number of moves to make all elements of the sequence zero.
- Translation of the work of Gauss where the fast Fourier transform algorithm first appeared
- sources about SVD complexity
Related Questions in GAME-THEORY
- Maximum number of guaranteed coins to get in a "30 coins in 3 boxes" puzzle
- Interesting number theoretical game
- Perfect Information Game and Chance node
- Valid operations to the value of a matrix game
- Rook Game Problem Solving
- Proof of Axiom of Transparency in Aumman's model of knowledge
- Sion's MinMax theorem over matrices
- Can Zermelo's theorem be extended to a game which always has a winner?
- a risk lover agent behave as if risk natural.
- How to prove that a strategy profile is a Proper Equilibrium?
Related Questions in MATCHING-THEORY
- Prove that a simple connected graph has even numbers of vertex
- Lexicographical covering of boolean poset
- Cantor-Bernstein-Schröder Theorem: small proof using Graph Theory, is this correct?
- All stable matchings of a given bipartite graph cover the same vertices.
- Maximum matching saturating a vertex
- Triangle inequality and graphs (min cost matching graph)
- Stable-Matching Algorithm with film upgrades
- Need help understanding stable matching proof
- Graph Theory - Matching
- Solving Quadratic program for finding perfect matching in polynomial time
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?
The approach using Irving's algorithm should be fine to prove no stable matching exists. If during phase one of the algorithm any participant is eventually rejected by all other participants, this indicates that no stable matching is possible. For the rankings in your problem, by Irving's algorithm we have
D has been rejected by all other participants and no stable matching is possible.
We can also reason about it by saying in any solution A, B, or C must be paired with D. For anyone who is with D, another person will have rated them highest, and D’s partner will prefer this other person over D. Also note that D is last on every persons preferences.