opal

Feb 13

Moduli of Curves I: A Curious Curve Count

Mathematical Gemstones

Young tableaux are to planes as labeled trees are to curves. This is the analogy from which I hope to start a series of posts on the beauty of the growing field of connections between the geometry of moduli spaces of curves, and combinatorics. What do the pictures above have in common? Two...

gemstones opal sapphire combinatorics algebraic geometry

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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