Kemnitz's Conjecture

In additive number theory, Kemnitz's conjecture states that every set of integer lattice points in the plane has a large subset whose centroid is also a lattice point.

Version

v1 · 2026-09-28 · History

Domain-specific #

10236

Domain group

Formal Sciences

Origin domain

Mathematics

Subdomains

Additive Number Theory, Combinatorics → Mathematics

Core Idea

Kemnitz's Conjecture is treated here as the recurring mathematics, logic, and statistics identity summarized by this source-grounded definition: In additive number theory, Kemnitz's conjecture states that every set of integer lattice points in the plane has a large subset whose centroid is also a lattice point. In additive number theory, Kemnitz's conjecture states that every set of integer lattice points in the plane has a large subset whose centroid is also a lattice point. It was proved independently in the autumn of 2003 by Christian Reiher, then an undergraduate student, and Carlos di Fiore, then.

Scope of Application

• Documented setting. In additive number theory, Kemnitz's conjecture states that every set of integer lattice points in the plane has a large subset whose centroid is also a lattice point.

• Documented setting. It was proved independently in the autumn of 2003 by Christian Reiher, then an undergraduate student, and Carlos di Fiore, then a high school student.

• Documented setting. Let n be a natural number and S a set of 4n-3 lattice points in plane.

• Documented setting. Then there exists a subset S1 \subseteq S with n points such that the centroid of all points from S1 is also a lattice point.

• Documented setting. Kemnitz's conjecture was formulated in 1983 by Arnfried Kemnitz as a generalization of the Erdős–Ginzburg–Ziv theorem, an analogous one-dimensional result stating that every 2n-1 integers have a subset of.

Clarity

A clear use of Kemnitz's Conjecture names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is In additive number theory, Kemnitz's conjecture states that every set of integer lattice points in the plane has a large subset whose centroid is also a lattice point.

Manages Complexity

Kemnitz's Conjecture compresses multiple mathematics, logic, and statistics details into a stable diagnostic relation. The source shows both the central mechanism—kemnitz's conjecture was formulated in 1983 by Arnfried Kemnitz as a generalization of the Erdős–Ginzburg–Ziv theorem, an analogous one-dimensional result stating that every 2n-1 integers have a subset of size n whose average is an integer.—and the practical consequence—in 2000, Lajos Rónyai proved a weakened.

Abstract Reasoning

1. Type the carrier. Identify the mathematics, logic, and statistics entities to which the claim applies.
2. State the relation. Use the source-grounded identity: In additive number theory, Kemnitz's conjecture states that every set of integer lattice points in the plane has a large subset whose centroid is also a lattice point.
3. Check operation and conditions. In additive number theory, Kemnitz's conjecture states that every set of integer lattice points in the plane has a large subset whose centroid is also a lattice point. 4.

Knowledge Transfer

Within the home domain. Knowledge about Kemnitz's Conjecture transfers literally when a new case preserves the same carrier type, relation, and recognition test. In additive number theory, Kemnitz's conjecture states that every set of integer lattice points in the plane has a large subset whose centroid is also a lattice point. It was proved independently in the autumn of 2003 by Christian Reiher, then an undergraduate student, and Carlos di Fiore, then a high school student. Beyond the home domain. No.

Neighborhood in Abstraction Space

Kemnitz's Conjecture sits in a sparse region of the domain-specific corpus (65^th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Number Theory & Packing Conjectures (5 abstractions)

Nearest neighbors

• Ulam's packing conjecture — 0.86
• Simplicial sphere — 0.84
• Local Analysis — 0.84
• Tensor product of fields — 0.84
• Divisor summatory function — 0.84

Computed from structural-signature embeddings · 2026-10-08