ABELIAN DIFFERENCE SETS AS LATTICE COVERINGS AND LATTICE TILINGS

DOI10.1017/S0004972721001271zbMath1497.05030OpenAlexW4206917776MaRDI QIDQ5867852

Mladen Kovačević

Publication date: 19 September 2022

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0004972721001271

zbMATH Keywords

tilingdifference setlattice packinglattice coveringgroup splittingManhattan metricprime power conjecture

Mathematics Subject Classification ID

Other combinatorial number theory (11B75) Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.) (05B10) Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17) Lattice packing and covering (number-theoretic aspects) (11H31) Combinatorial aspects of tessellation and tiling problems (05B45) Additive bases, including sumsets (11B13) Tilings in (n) dimensions (aspects of discrete geometry) (52C22) Combinatorial aspects of packing and covering (05B40)

Cites Work

• On multiple coverings of the infinite rectangular grid with balls of constant radius
• Translational tilings by a polytope, with multiplicity
• Codes in the Space of Multisets—Coding for Permutation Channels With Impairments
• A Theorem in Finite Projective Geometry and Some Applications to Number Theory
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