What is recorded here?
The number of cyclic binary sequences of length 2^n containing each binary word of length n exactly once is 2^(2^(n-1)-n). The proof relates these cycles to complete directed walks and shows that doubling a two-in/two-out network with m vertices multiplies its cyclic complete-walk count by 2^(m-1).
Source-linked catalogue note. A detailed explanatory guide has not yet been prepared for this entry.
Scientific scope
Cyclic rotations are identified, but reversal is not identified; changing these conventions changes the count. The binary count resolves the conjecture explicitly credited to K. Posthumus. It is not a source-backed claim of first discovery of all universal cycles, nor the general-alphabet formula or full later BEST theorem.
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People and systems
N. G. de Bruijn
Source-listed authors for the exact contribution; experimental subjects are not autonomous scientific authors. Source support and predecessor work retain separate roles. Individual effort shares and unresolved identities are not inferred.
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English catalogue narrative
de Bruijn counts binary cycles containing every length-n word once
The number of cyclic binary sequences of length 2^n containing each binary word of length n exactly once is 2^(2^(n-1)-n). The proof relates these cycles to complete directed walks and shows that doubling a two-in/two-out network with m vertices multiplies its cyclic complete-walk count by 2^(m-1).
Scientific scope
Cyclic rotations are identified, but reversal is not identified; changing these conventions changes the count. The binary count resolves the conjecture explicitly credited to K. Posthumus. It is not a source-backed claim of first discovery of all universal cycles, nor the general-alphabet formula or full later BEST theorem.
Reading status
This is a source-linked WRS catalogue note. A full explanatory guide and independent scientific reconstruction have not been completed for this entry. Read the identified original work for its complete narrative and arguments.
People and systems
N. G. de Bruijn
Source-listed authors for the exact contribution; experimental subjects are not autonomous scientific authors. Source support and predecessor work retain separate roles. Individual effort shares and unresolved identities are not inferred.