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3-Term Progression-Free Subsets of $[n]$ by Size and Sum: A Low-Sum Recurrence and a Central-Sum Parity
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October 01, 2026 19:18
3-Term Progression-Free Subsets of $[n]$ by Size and Sum: A Low-Sum Recurrence and a Central-Sum Parity
This paper proves two verified enumerative statements about $3$-term arithmetic progression-free subsets of $[n]$, refined by cardinality and element sum. First, small-sum progression-free sets satisfy Pascal's recurrence exactly under an …
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