How do you canonicalize a matrix over column- and row-swap operations? Or more specifically, does there exist a function f(M) such that f(M)=f(N) iff there is set of column- and row-swap operations (i.e. a permutation matrix A) on M that would transform M into N (i.e. AMA’)? @Coffeemath and I are discussing a few ways […]

Let $A$ be a sudoku-matrix. Assume that its determinant is positive. What is the lowest, what the highest possible value for the determinant of $A$ ? $A$ must have the dominant eigenvalue $45$, but this does not seem to help establishing bounds. My records so far : $$\pmatrix{7&2&9&6&4&3&5&1&8 \\ 5&6&8&9&1&2&7&4&3 \\ 1&3&4&8&5&7&9&6&2 \\ 2&8&7&4&6&1&3&9&5 \\ […]

I want to know if the popular Sudoku puzzle is a Cayley table for a group. Methods I’ve looked at: Someone I’ve spoken to told me they’re not because counting the number of puzzle solutions against the number of tables with certain permutations of elements, rows and columns, the solutions are bigger than the tables, […]

Intereting Posts

Matrix exponential convergence
Riemann sum on infinite interval
Integral domain with a finitely generated non-zero injective module is a field
Every preorder is a topological space
Sources on Several Complex Variables
Find integers $(w, x, y, z)$ such that the product of each two of them minus 1 is square.
uniqueness of solutions of $ax=b$ and $ya=b$ in a semigroup .
Proving $\int_{0}^{\pi/2}x\sqrt{\tan{x}}\log{\sin{x}}\,\mathrm dx=-\frac{\pi\sqrt{2}}{48}(\pi^2+12\pi \log{2}+24\log^2{2}) $
How to get the co-ordinates of scaled down polygon
Congruence question with divisibility
For $n \in \mathbb{N}$ $\lfloor{\sqrt{n} + \sqrt{n+1}\rfloor} = \lfloor{\sqrt{4n+2}\rfloor}$
Let $X$ and $Y$ be countable sets. Then $X\cup Y$ is countable
Proof of fundamental lemma of calculus of variation.
Inverse of $x\log(x)$ for $x>1$
Evans pde book: details on an bound for a Sobolev norm in the proof of the Meyers-Serrin theorem