- combinatorics (4),
- functional-analysis (1),
- graph-theory (2),
- group-theory (2),
- number-theory (2),
- optimization (1),
- recreational-mathematics (4)
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Cumulative XOR via the shift operator on $\mathbb{F}_2^\infty$
A closed form for the prefix bitwise XOR, proved by telescoping against the unilateral shift on the sequence space $\mathbb{F}_2^\infty$.
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IMO 1981/2 via generating functions
A generating-functions proof that the average minimum of an r-subset of {1,...,n} is (n+1)/(r+1).
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SKMO 2026/1 via KKT conditions
Solving a problem from SKMO with the Karush–Kuhn–Tucker conditions.
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Infinity of primes
A group-theoretic proof of infinity of primes.
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Orbit counting lemma
A graph-theoretic proof of the orbit-counting theorem.