combinatorics / Additive Combinatorics, Zero-Sum Theory
Godara and Sarkar proved $\mathsf{d}(H_{27})=6$ for the exponent-$p$ Heisenberg group and posed $\mathsf{d}(H_{p^3})=3p-3$ for every odd prime $p$, leaving $p\ge5$ open. The paper settles the first open case, $\mathsf{d}(H_{125})=12$, the upper bound reducing to a finite spread bound verified by exhaustive search and independently reproduced.
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Settles the case p=5. The posed formula for every odd prime remains open.
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Godara and Sarkar proved $\mathsf{d}(H_{27})=6$ for the exponent-$p$ Heisenberg group and posed $\mathsf{d}(H_{p^3})=3p-3$ for every odd prime $p$, leaving $p\ge5$ open. The paper settles the first open case, $\mathsf{d}(H_{125})=12$, the upper bound reducing to a finite spread bound verified by exhaustive search and independently reproduced.
Settles the case p=5. The posed formula for every odd prime remains open.
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