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## 3 ON THE HEREDITARY DISCREPANCY OF HOMOGENEOUS ARITHMETIC PROGRESSIONS

Citations: | 3 - 1 self |

### Citations

61 | Some unsolved problems.
- Erdos
- 1961
(Show Context)
Citation Context ...via proving an exponential lower bound on the discrepancy of set systems of subcubes of the boolean cube {0, 1}d. 1. Introduction Circa 1932 Paul Erdős made the following conjecture: Conjecture 1.1 (=-=[2]-=-). For any function f : N → {−1,+1} and for any constant C, there exist positive integers n and a such that | ⌊n/a⌋∑ i=1 f(ia)| > C. In modern terms, the maximum value of ∑k i=1 f(ia) over all a and a... |

49 |
Discrepancy of setsystems and matrices
- Lovász, Spencer, et al.
- 1986
(Show Context)
Citation Context ...homogeneous arithmetic progressions. We prove a lower bound on the set system of boolean subcubes using the determinant lower bound on hereditary discrepancy due to Lovász, Spencer, and Vesztergombi =-=[6]-=-. Such systems of boolean subcubes were previously considered in computer science in the context of private data analysis [5, 8]. Our construction produces sets Wn of square free integers with a large... |

39 | The Price of Privately Releasing Contingency Tables and the Spectra of Random Matrices with Correlated Rows
- KASIVISWANATHAN, RUDELSON, et al.
(Show Context)
Citation Context ... bound on hereditary discrepancy due to Lovász, Spencer, and Vesztergombi [6]. Such systems of boolean subcubes were previously considered in computer science in the context of private data analysis =-=[5, 8]-=-. Our construction produces sets Wn of square free integers with a large number of prime divisors, suggesting that such integers are a chief obstacle in achieving bounded discrepancy for homogeneous a... |

6 |
Aleksandar Nikolov, Optimal private halfspace counting via discrepancy
- Muthukrishnan
(Show Context)
Citation Context ... boolean cube. Such set systems have applications in the theory of differential privacy. The proof of Lemma 3.2 together with the connection between discrepancy and differential privacy formalized in =-=[7]-=- can be used to give simpler proofs of the noise lower bounds of the type considered in [5]. It is an interesting question whether discrepancy bounds on set systems of boolean subcubes can find other ... |

2 |
Erdős discrepancy problem 22
- Kalai
(Show Context)
Citation Context ... discrepancy problem recently received attention as the subject of the fifth polymath project [1]. Our note is motivated by recent results of Alon and Kalai, announced and sketched in the weblog post =-=[4]-=-. Using the Beck-Fiala theorem, they showed that even for homogeneous arithmetic progressions restricted to an arbitrary subset of the integers up to n, the discrepancy is no more than n1/Ω(log logn).... |

2 |
Row products of random matrices, Arxiv preprint arXiv:1102.1947
- Rudelson
- 2011
(Show Context)
Citation Context ... bound on hereditary discrepancy due to Lovász, Spencer, and Vesztergombi [6]. Such systems of boolean subcubes were previously considered in computer science in the context of private data analysis =-=[5, 8]-=-. Our construction produces sets Wn of square free integers with a large number of prime divisors, suggesting that such integers are a chief obstacle in achieving bounded discrepancy for homogeneous a... |

1 | Two-colorings of positive integers
- Finch
(Show Context)
Citation Context ...e f(i) = −1 if and only if the last nonzero digit of i in ternary representation is 2 has discrepancy O(log n). For references and other partial results related to the Erdős discrepancy problem, see =-=[3, 1]-=-. The Erdős discrepancy problem recently received attention as the subject of the fifth polymath project [1]. Our note is motivated by recent results of Alon and Kalai, announced and sketched in the ... |