combinatorics / Boolean functions; combinatorial number theory
With $N = 2^k - 1$ and $\mathrm{wt}(n)$ the binary Hamming weight, Tu and Deng conjectured that for every $1 \leq t \leq N-1$ at most $2^{k-1}$ pairs $(a,b)$ satisfy $a + b \equiv t \pmod N$ and $\mathrm{wt}(a) + \mathrm{wt}(b) < k$. Proved in full.
Temporal state
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Append-only history
With $N = 2^k - 1$ and $\mathrm{wt}(n)$ the binary Hamming weight, Tu and Deng conjectured that for every $1 \leq t \leq N-1$ at most $2^{k-1}$ pairs $(a,b)$ satisfy $a + b \equiv t \pmod N$ and $\mathrm{wt}(a) + \mathrm{wt}(b) < k$. Proved in full.
Research memory
With $N = 2^k - 1$ and $\mathrm{wt}(n)$ the binary Hamming weight, Tu and Deng conjectured that for every $1 \leq t \leq N-1$ at most $2^{k-1}$ pairs $(a,b)$ satisfy $a + b \equiv t \pmod N$ and $\mathrm{wt}(a) + \mathrm{wt}(b) < k$. Proved in full.
Evidence graph
depends on · problem · claimed