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A graceful labeling of a connected simple undirected graph $G=(V,E)$ is a map $f:V\to\lbrace 1,...,|E|+1\rbrace$ such that for all $t\in\lbrace 1,...,|E|\rbrace$ there is a (trivially unique) $\langle ...

I was able to find (and prove) arrangements that would result in the sum of the products of adjacent pairs attain the maximum. I am able to conjecture that the arrangement that would result in the ...

I know this: There are two non-degenerate quadratic forms on $GF(2)^2r$. The hyperbolic form may be taken to be $Q^+(x)=x_0 x_1 + \cdots +x_{2r-2}x_{2r-1}$ , and the elliptic form to be $Q^-(x)=x^...

Let me start with a question for which I know the answer. Consider a symmetric integral $n\times n$ matrix $A=(a_{ij})$ such that $a_{ii}=2$, and for $i\ne j$ one has $a_{ij}=0$ or $-1$. One can ...