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A Counting Lemma for Somewhat Restricted 3-APs
Amey Bhangale, Subhash Khot, Yang P. Liu +1
For a prime , a somewhat restricted -AP in is a triplet , where and . We prove a counting lemma fo…
Isoperimetric Inequalities Made Simpler
Ronen Eldan, Guy Kindler, Noam Lifshitz +1
We give an alternative, simple method to prove isoperimetric inequalities over the hypercube. In particular, we show: 1. An elementary proof of classical isoperimetric inequalities…
Effective Bounds for Restricted -Arithmetic Progressions in
Amey Bhangale, Subhash Khot, Dor Minzer
For a prime , a restricted arithmetic progression in is a triplet of vectors in which the common difference is a non-zero element from $\{0,1…
Reasonable Bounds for Combinatorial Lines of Length Three
Amey Bhangale, Subhash Khot, Yang P. Liu +1
We prove that any subset with contains a combinatorial line of length , i.e., , not all equal, with…
A Dense Model Theorem for the Boolean Slice
Gil Kalai, Noam Lifshitz, Dor Minzer +1
The (low soundness) linearity testing problem for the middle slice of the Boolean cube is as follows. Let and be a function on the middle slice on the Boolean c…
Product Mixing in Compact Lie Groups
David Ellis, Guy Kindler, Noam Lifshitz +1
If is a group, we say a subset of is product-free if the equation has no solutions with . For , a group is said to be -quas…