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• W3132420565 abstract "Abstract We prove that the volume of central hyperplane sections of a unit cube in $mathbb{R}^n$ orthogonal to a main diagonal of the cube is a strictly monotonically increasing function of the dimension for $ngeq 3$. Our argument uses an integral formula that goes back to Pólya [ 20] (see also [ 14] and [ 3]) for the volume of central sections of the cube and Laplace’s method to estimate the asymptotic behavior of the integral. First, we show that monotonicity holds starting from some specific $n_0$. Then, using interval arithmetic and automatic differentiation, we compute an explicit bound for $n_0$ and check the remaining cases between $3$ and $n_0$ by direct computation." @default.
• W3132420565 created "2021-03-01" @default.
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• W3132420565 date "2020-10-17" @default.
• W3132420565 modified "2023-10-16" @default.
• W3132420565 title "Central Diagonal Sections of the n-Cube" @default.
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• W3132420565 doi "https://doi.org/10.1093/imrn/rnaa254" @default.
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