Discrete Brunn–Minkowski inequality for subsets of the cube

Lars Becker; Paata Ivanisvili; Dmitry Krachun; José Madrid

doi:10.1007/s00493-025-00180-0

Discrete Brunn–Minkowski inequality for subsets of the cube

Lars Becker
, Paata Ivanisvili
, Dmitry Krachun
, José Madrid

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We show that for all A,B⊆{0,1,2}d we have (Formula presented.) We also show that for all finite A,B⊂Zd, and any V⊆{0,1}d the inequality (Formula presented.) holds for all p∈(1,∞), where q=pp-1 is the conjugate exponent of p. All the estimates are dimension free with the best possible exponents. We discuss applications to various related problems.

Original language	English (US)
Article number	48
Journal	Combinatorica
Volume	45
Issue number	5
DOIs	https://doi.org/10.1007/s00493-025-00180-0
State	Published - Oct 2025

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics
Computational Mathematics

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10.1007/s00493-025-00180-0

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abstract = "We show that for all A,B⊆\{0,1,2\}d we have (Formula presented.) We also show that for all finite A,B⊂Zd, and any V⊆\{0,1\}d the inequality (Formula presented.) holds for all p∈(1,∞), where q=pp-1 is the conjugate exponent of p. All the estimates are dimension free with the best possible exponents. We discuss applications to various related problems.",

author = "Lars Becker and Paata Ivanisvili and Dmitry Krachun and Jos{\'e} Madrid",

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AU - Becker, Lars

AU - Ivanisvili, Paata

AU - Krachun, Dmitry

AU - Madrid, José

N1 - Publisher Copyright: © The Author(s), under exclusive licence to János Bolyai Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2025.

PY - 2025/10

Y1 - 2025/10

N2 - We show that for all A,B⊆{0,1,2}d we have (Formula presented.) We also show that for all finite A,B⊂Zd, and any V⊆{0,1}d the inequality (Formula presented.) holds for all p∈(1,∞), where q=pp-1 is the conjugate exponent of p. All the estimates are dimension free with the best possible exponents. We discuss applications to various related problems.

AB - We show that for all A,B⊆{0,1,2}d we have (Formula presented.) We also show that for all finite A,B⊂Zd, and any V⊆{0,1}d the inequality (Formula presented.) holds for all p∈(1,∞), where q=pp-1 is the conjugate exponent of p. All the estimates are dimension free with the best possible exponents. We discuss applications to various related problems.

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UR - https://www.scopus.com/pages/publications/105017475455#tab=citedBy

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DO - 10.1007/s00493-025-00180-0

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JO - Combinatorica

JF - Combinatorica

IS - 5

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ER -

Discrete Brunn–Minkowski inequality for subsets of the cube

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