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Questions on the subject additive combinatorics, also known as arithmetic combinatorics, such as questions on: additive bases, sum sets, inverse sum set theorems, sets with small doubling, Sidon sets, Szemerédi's theorem and its ramifications, Gowers uniformity norms, etc. Often combined with the top-level tags nt.number-theory or co.combinatorics. Some additional tags are available for further specialization, including the tags sumsets and sidon-sets.
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Ordered lattice point enumeration
I am going to try to answer the version of the Observation which seems to imply that the original "orthogonal" basis condition really is meant to mean "positive multiples of the standard basis vectors …