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Results tagged with co.combinatorics
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user 51424
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
14
votes
What exact number of domino tilings cannot be realizable?
Consider a $4\times 2k+1$ rectangle. Label its points by $(x,y)$, with $x$ from $0$ to $3$ and $y$ from $0$ to $2k.$ Remove from the rectangle the points $(1,y)$ and $(2,y)$ for $y$ odd. I claim that …
- 5,958
13
votes
Alice and Bob playing on a circle
Here is an argument that Alice wins for odd $n$. Label the points $1$ to $n.$
Lemma: If at any point Alice has marked $k$ points in a row and no other points, Bob has marked the two points immediatel …
- 5,958
9
votes
Accepted
Simple question about polynomials
This equation has no solutions when $d$ is odd. (EDIT: See below for the general case.)
Actually, for $d$ odd, there are no triples $(F_0,F_1,F_2)$ with $F_1\cdot F_2-F_0^2$ a multiple of $x$, let al …
- 5,958