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Stability and exact Turan numbers for matroids

机译:达到稳定性和炎症的精确暗影号码

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We consider the Turan-type problem of bounding the size of a set M subset of F-2(n) that does not contain a linear copy of a given fixed set N subset of F-2(k), where n is large compared to k. An Erdos-Stone type theorem [5] in this setting gives a bound that is tight up to a o(2(n)) error term; our first main result gives a stability version of this theorem, showing that such an M that is close in size to the upper bound in [5] is close to the obvious extremal example in the sense of symmetric difference. Our second result shows that the error term in [5] is exactly controlled by the solution to one of a class of 'sparse' extremal problems, and gives some examples where the error term can be eliminated completely to give a sharp upper bound on vertical bar M vertical bar. Crown Copyright (C) 2019 Published by Elsevier Inc. All rights reserved.
机译:我们考虑绑定的MATAN型问题的MITAN-2(n)的尺寸不包含f-2(k)的给定固定集n子集的线性副本,其中n比较大 k。 此设置中的Erdos-Stone类型定理[5]给出了紧密到O(2(n))错误项的绑定; 我们的第一个主要结果提供了本定理的稳定性版本,表明这种在[5]中的上限尺寸尺寸的m是靠近对称差异感的明显极值示例。 我们的第二个结果表明,[5]中的错误术语由解决方案与一类“稀疏”的极值问题的一个完全控制,并给出了一些示例,其中可以完全消除错误项以在垂直上给出尖锐的上限 条垂直栏。 2019年Elsevier Inc.版权所有的皇家版权(c)2019年保留所有权利。

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