What is recorded here?
Extending the Croot–Lev–Pach polynomial method, the paper gives an exponentially smaller-than-q^n bound for three-term-progression-free subsets of finite-field vector spaces in the applicable odd-characteristic setting. In F_3^n it obtains a cap-set bound with exponential base below 2.756.
Source-linked catalogue note. A detailed explanatory guide has not yet been prepared for this entry.
Scientific scope
This is an upper bound, not the exact largest cap size, and it does not transfer the same exponential saving to cyclic integer intervals. The joint paper states that the two authors developed essentially identical arguments independently. Predecessor polynomial methods retain their separate credit.
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People and systems
Jordan S. Ellenberg; Dion Gijswijt
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
Ellenberg and Gijswijt: exponential upper bounds for progression-free finite-field sets
Extending the Croot–Lev–Pach polynomial method, the paper gives an exponentially smaller-than-q^n bound for three-term-progression-free subsets of finite-field vector spaces in the applicable odd-characteristic setting. In F_3^n it obtains a cap-set bound with exponential base below 2.756.
Scientific scope
This is an upper bound, not the exact largest cap size, and it does not transfer the same exponential saving to cyclic integer intervals. The joint paper states that the two authors developed essentially identical arguments independently. Predecessor polynomial methods retain their separate credit.
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
Jordan S. Ellenberg; Dion Gijswijt
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.