9 votes

Shortest almost trivial element of free group

Repeating from the comments section: This (natural and beautiful) question was previously asked and answered on this site. See Collapsible group words. It also appeared recently on math.se. The ...
Sean Eberhard's user avatar
5 votes

Exhaustive list of small graphs for which $\frac{\alpha(G)\omega(G)}{n}$ is small?

See http://users.cecs.anu.edu.au/~bdm/data/ramsey.html , which contains maximum Ramsey graphs. Ramsey graphs are closely linked to your problem, because the largest graph with $\alpha(G) = a, \omega(G)...
Command Master's user avatar
5 votes

Permutation of a mixture of (anti)commuting variables and consistency issue regarding the sign

If you have a rewriting $\sigma\cdot a\to a$ following your (anti-)commutation rules, remove all the bosonic variables. Then you still have a valid rewriting $\sigma'\cdot f\to f$. Now if there were a ...
Christian Remling's user avatar
3 votes

Number of Salem–Spencer subsets of $\{1,2,3,\dots ,n\}$

Fix a smallish integer $m$, and assume for simplicity that $n$ is a multiple of $m$. Break $\{1,\dots,n\}$ into $n/m$ consecutive intervals of $m$ consecutive integers each. Each such interval must ...
Greg Martin's user avatar
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1 vote

Sums of products over restricted set compositions

Here are some hopefully not too involute thoughts for a quite general form of weights, inspired by a similar particular computation. To be slightly more general, suppose we are multiplying some sums ...
Pietro Majer's user avatar

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