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combinatorics

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A dropped digit sat in an OEIS entry for years until a Claude agent spotted it. What that means for anyone who copies values from reference tables.
WritingWhat a long-standing error in a math database means for anyone who copies reference values· Oct 24, 2026
Checking an Erdős conjecture on every tree up to a size rules out small counterexamples but does not prove it. What such a check shows and how it is made.
WritingWhy checking a math conjecture on every case up to a size is not a proof· Oct 24, 2026
A network puzzle: pick as few points as possible so that every point is picked or linked to a picked one. A search I ran with Claude found a smaller set than any published.
WritingA new best-known dominating set for the twelfth Fibonacci cube, and a month-long solver run that returned no answer· Sep 26, 2026
Every run first had to reproduce the expert's published tables exactly. That let him check the new work on his own machines instead of taking my word for it.
WritingExtending an expert's tables for unsolved take-away games in a way he could check himself· Jul 16, 2026· 3 versions
A number in the OEIS, a public database of number sequences, had a dropped digit for over a decade. A Claude agent spotted it; the right value was confirmed by two separate routes and the entry corrected.
WritingHow I found and fixed a number that was wrong in the OEIS for over a decade· Jul 13, 2026
The first count I could find of labeled dependency charts (directed acyclic graphs) in which each task waits on at most k others, for small caps k, with proved formulas, now in the OEIS.
WritingCounting dependency charts where each task depends on at most two or three others, and a pattern in the counts that someone else later proved· Jul 5, 2026

Result3

An Erdős conjecture: in every tree, the number of ways to pick k dots with no two joined rises, then falls, as k grows. I checked every tree three sizes past the old limit; it held.
RecordPublishedChecking an Erdős conjecture on every tree, three sizes further than before· Aug 4, 2026
In July I pushed the published tables for a set of unsolved take-away games two to four times further. In four of the games, new heap sizes with rare values turned up.
RecordPublishedExtending the tables for a set of unsolved take-away games, checked and built on by the expert who keeps them· Jul 16, 2026· 3 versions
The largest table from the July take-away game work, taken four times past its published end after first reproducing the old table exactly. No new rare value appeared.
RecordPublishedExtending the table for one unsolved take-away game to four times its published length· Jul 5, 2026· 2 versions