1. Introduction
   • Starting the blog
   • Boolean circuits as a model of computation
     • (1), (2)
   • The sunflower lemma and \(\Gamma\)-condition
   • Room for improvement
   • The extension generator theorem (EGT)
     • (1), (2)
2. Overview of the first proof of the sunflower conjecture
   • Paper 1 posted on the left includes the same error as Paper 2 I’m trying to fix right now. See the last three posts of this chapter for more details. Hopefully I can upload the next version of the two papers soon.
   • The split lemma
   • The main idea
   • Construction algorithms
     • (1), (2), (3)
   • The two recursive statements
     • (1), (2), (3)
   • Step 1 of proving (2.1)
   • An error in Step 1
   • Having figured out the proof error, I’ve restarted the blog trying to fix it (6/9/23).
   • Restarting with an error overview
   • Step 2 of proving (2.1)
3.  On the combinatorial domain \(2^X\) (Part 1)
   • Sparsity of a family
     • (1), (2), (3), (4), (5)
   • Proof of the EGT
     • (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12)
   • Collective \( \Gamma \)-conditions
     • (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14), (15), (16)  
   • Partitioning sets and families
     • (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14), (15)
4. Three disjoint sets in \({\mathcal F} \) with \( \Gamma( m^{\frac{1}{2}+\epsilon} ) \)
   • The push-up lemma
     • (1), (2), (3), (4), (5), (6), (7)  
   • Main recursive steps
5. On the combinatorial domain \(2^X\) (Part 2)
   • Limit of extension generators
   • Generating sets by disjointness
   • Extensions and shadows
   • The Hamming distance between two families
6. EGT and circuit complexity
   • Circuit complexity and the P vs NP problem
   • Random vertex coloring: the standard method for monotone complexity
   • Application of EGT to circuit complexity: overview of Paper 4

Links for mobile devices

• Paper S4
• Paper 3
• Paper S3
• Index page