On sets of large doubling, (4) sets, and error-correcting codes
Allison LewkoMark Lewko Columbia University Institute for Advanced
Study TexPoint fonts used in EMF. Read the TexPoint manual before
you delete this box.: A AAA Doubling of Sets Sets of Large Doubling
A First Attempt at a Structure Theorem Connection to (4) Sets A
Question of Rudin [Rudin, 1960] Is every (4) set a finite union of
B 2 [G] sets? Meyers Set [M68] Ramseys Theorem (1, 2) (2, 5) (1,
13) (23, 42) (13, 33) (8,10) (5, 12) Meyers Set (contd.)... (1, 2)
(2, 5) (1, 13) (23, 42) (5, 12) Meyers Set (contd.) Third Attempt
at a Structure Theorem Some Related Questions Attacking the
Incompressible Union Problem... Properties of This Construction a +
b Properties of This Construction Recall: Ramseys Theorem (1, 2, 3,
4) (2, 5, 6, 10) (1, 2, 4, 13) (7, 19, 23, 42) (3, 11, 13, 33) (4,
8, 9, 10) (5, 12, 24, 73) Properties of the Construction Refining
the Approach a + b Reed-Solomon Codes B 2 [1] Set Building
Blocks... B 2 [1] Set Building Blocks Assembling the Blocks
Hadamard Matrices Summary of the Construction... Proof of
Incompressibility Implications of Construction Open Problems Is
every Sidon set a finite union of independent sets? What about a
structure theorem for large doubling sets by moving beyond B 2 [G]
sets? Thanks! Questions?
