Name
Abstract | ||
|---|---|---|
We initiate the study of Boolean function analysis on high-dimensional expanders. We describe an analog of the Fourier expansion and of the Fourier levels on simplicial complexes, and generalize the FKN theorem to high-dimensional expanders. Our results demonstrate that a high-dimensional expanding complex $X$ can sometimes serve as a sparse model for the Boolean slice or hypercube, and quite possibly additional results from Boolean function analysis can be carried over to this sparse model. Therefore, this model can be viewed as a derandomization of the Boolean slice, containing $|X(k)|=O(n)$ points in comparison to $binom{n}{k+1}$ points in the $(k+1)$-slice (which consists of all $n$-bit strings with exactly $k+1$ ones). |
Year | Venue | Field |
|---|---|---|
2018 | arXiv: Computational Complexity | Boolean function,Discrete mathematics,Combinatorics,Unique games conjecture,Random walk,Sparse model,Fourier transform,Fourier series,Mathematics,Hypercube,Partially ordered set |
DocType | Volume | Citations |
Journal | abs/1804.08155 | 0 |
PageRank | References | Authors |
0.34 | 22 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yotam Dikstein | 1 | 1 | 1.03 |
| Irit Dinur | 2 | 1187 | 85.67 |
| Yuval Filmus | 3 | 275 | 27.33 |
| Prahladh Harsha | 4 | 371 | 32.06 |