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 Yearling
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Jan
24
comment The hardest game of mahjongg
I think you need to address the issue of how to lay out the tiles for arbitrary $n$ before it even makes sense to start thinking about an answer.
Jan
15
comment Maximal tiling without any 3-in-a-rows
@randomra, if the maximum Hamming weight which can be achieved in an $m\times n$ rectangle is $w$ then that gives an upper bound for the density of any infinite tiling of $\frac{w}{mn}$ by the simple mechanism of superimposing an $m \times n$ grid over the infinite tiling.
Jan
12
awarded  Yearling
Jan
9
comment Maximal tiling without any 3-in-a-rows
The existence of (non-tiling) moderately large squares with densities > 1/2 (e.g. 15x15 with 114 bits set) indicates that the case analysis would have to work on larger units than those squares. I very much doubt that the number of cases for this type of approach would be computationally tractable.
Jan
9
comment Maximal tiling without any 3-in-a-rows
I don't understand the argument that cases can be eliminated by the symmetry of swapping 0s and 1s: that's not a symmetry, because 000 is allowed and 111 isn't. I also don't understand what contradiction you see in your first example.
Jan
9
revised Maximal tiling without any 3-in-a-rows
added 75 characters in body
Jan
8
revised Maximal tiling without any 3-in-a-rows
deleted 243 characters in body
Dec
12
comment If $x^n$ is ivertible in a ring show that $x$ is invertible.
So to be precise, your question is how to show that, given a left inverse of $x$ and a right inverse of $x$, the two must be the same even in a non-commutative ring?
Nov
30
comment Erdős and Szemerédi sums and producs
Note: this looks suspiciously like a certain active contest.
Nov
28
reviewed Reject Find the Probability mass function(a grid with p-values in the cells)
Nov
28
reviewed Close First Order Logic problem with Compactness theorem
Nov
28
reviewed Close formula for series the 0,1,0,1,0,1,… With certain laws
Nov
28
reviewed Close Probability that two independent samples, each one without repetition, share K elements
Nov
28
reviewed Close Verifying that $T_0 = F, T_n = 0$ is a universal $\delta$-functor
Nov
28
reviewed Close On the meaning of “or” in logic
Nov
28
answered name or characterization for the “partition” lattice of integer partitions of some n? (Young lattice row partial order)
Nov
27
answered Maximal tiling without any 3-in-a-rows
Nov
18
reviewed Close Is the graph of $xy=1$ in $\mathbb C^{2}$ connected?
Nov
18
reviewed Close Limit value of a sequence
Nov
13
reviewed Close Find the center and radius of the circle whose equation is $x^ 2 + y^ 2 - 6x - 2y + 4 = 0$