number-theory / Number Theory, Covering Systems
For irreducible covering sets of size $k$, determine their count, the possible largest modulus, the maximal reciprocal sum, and whether divisor-set examples occur infinitely often.
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exact largest modulus 3·2^{k-3} for k ≥ 5, near-linear least maximum, reciprocal mass Θ(log k), and an infinite divisor family; the counting asymptotic rests on the cited BBMST theorem
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For irreducible covering sets of size $k$, determine their count, the possible largest modulus, the maximal reciprocal sum, and whether divisor-set examples occur infinitely often.
exact largest modulus 3·2^{k-3} for k ≥ 5, near-linear least maximum, reciprocal mass Θ(log k), and an infinite divisor family; the counting asymptotic rests on the cited BBMST theorem
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