On the Linear and Hereditary Discrepancies
نویسندگان
چکیده
منابع مشابه
On the Linear and Hereditary Discrepancies
We exhibit a set system S 0 such that any set system containing it has linear discrepancy at least 2. Let V be a nite set and S 2 V a system of subsets of V. The incidence matrix A of (V; S) has rows indexed by the sets of S and the columns indexed by the points of V. The column corresponding to a point v 2 V is denoted by a v. A coloring of V is a mapping : V ! f?1; +1g. The discrepancy of S, ...
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Let A be a m n{matrix. Linear and hereditary discrepancy are deened as lindisc(A) := maxfminfkA(p ")k 1 j " 2 ff1; 1g n g jp 2 1; 1] n g herdisc(A) := maxfminfk(a ij) i2m];j2J "k 1 j " 2 ff1; 1g n g jJ n]g: We're investigating connections between the two concepts. Best results known are lindisc(A) 2(1 2 2 n) herdisc(A) for any matrix A and an example of an A satisfying lindisc(A) = 2(1 1 n+1) h...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2000
ISSN: 0195-6698
DOI: 10.1006/eujc.1999.0361