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Latest Paper Draft (About 1.4MByte)

Links to the first version

Paper Verson 1.11 ,  Explanatory Notes Version 1.11 ,  Overview of the Shift Method (1.086MByte)

Google Docs for extra explanations to the 1st version

Sections 2 and 3

l-Extension,  Counting Marks,  Double Marks and Lemma 2.5Extension Generator Theorem 1,  Definition of Extension GeneratorEGT2  EGT3 ,  EGT4 , Split y of [n],  Relation to Sunflower .

Section 4

DNF and Terms I,  DNF and Terms II,   Preprocess,   Quadruples σ, 

BlockedEdges I,   BlockedEdges IIBlockedEdges III, 

LocalShiftLemma by Lemma,

Edge Direction ProblemRegular σ Only.

Section 5

Clique-Tail Pairs,  Fixed Point of (z, z’)First Two StepsSpace-Proportional Splits Step 3

Links to Hamming Space papers

l-extension Ext(U, l) becomes a majority when m is small and U is not too sparse  (Congressus Numerantium, 173(2005), 33–41)

Hamming Distance between Two Not Too Sparse m-Set Families is O( m / exp(-ln2 ln m) ), (Full version of the paper posted on 8/26/12. It improves the bound from O( m / ln m ). )

The sparsity of l-shadow of U is small as l gets smaller than m (Congressus Numerantium, 168(2004), 21–31. The definition of Ext(U, l) is slightly different in this old paper. It’s due to my try-and-errors.)

Some basic claims related to the Hamming space  (Congressus Numerantium, 161(2003), 41–63. )


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