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arXiv · 2512.06587

Proof of a combinatorial conjecture posed in "The Blimpy Shape of Heady-s and Taily-s Bit Strings"

Bruce Levin
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Abstract

We demonstrate three properties conjectured to hold for a certain function by Levin (2025) in a study of the blimpy graphical shape of the number of bit strings with a given score under an interesting scoring system. The properties include discrete convexity, a simple formula for the greatest argument at which the function is negative, and a positive expectation under a certain probability function. A new set of inequalities which imply the latter is presented and proved under some monotonicity assumptions.

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Bruce Levin. 2026-02-10. Proof of a combinatorial conjecture posed in "The Blimpy Shape of Heady-s and Taily-s Bit Strings". https://arxiv.org/abs/2512.06587

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