bijective proof

Jan 07 2024

How many trivalent trees does it take to hold up a moduli space?

Mathematical Gemstones

After a bit of a hiatus due to difficulties with Wordpress, Mathematical Gemstones is back! Feel free to browse the new layout. Today’s post introduces moduli spaces of curves, and one of the many ways combinatorial gemstones arise in this vast area of algebraic geometry. A brief motivating...

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Aug 07 2022

Sorting sets of binary strings into threes

Mathematical Gemstones

Time for a just-for-fun combinatorial problem! Thanks to my brother Kenneth Monks for suggesting it. Consider the numbers of the form $2^{2^n}-1$ for positive integers $n$. The first few, for $n=1,2,3,4,\ldots$, are: \[3, 15, 255, 65535, \ldots\] One thing that all of these numbers have in...

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