论文标题
反向部分贪婪基础的较大贪婪总和
Larger Greedy Sums for Reverse Partially Greedy Bases
论文作者
论文摘要
由于Dilworth等人而引起的一个有趣的结果。是，如果我们在定义贪婪财产的条件下以常数因子$λ> 1 $扩大贪婪的总和，那么我们获得了几乎贪婪的财产的等效性，这是一个严格的弱属性。以前，本文的作者表明，在定义部分贪婪（PG）财产的条件下，将贪婪的总和扩大到$λ$，也严格削弱了该财产。但是，迪尔沃思（Dilworth）和库拉纳（Khurana）的反向部分贪婪（RPG）基础的定义中，贪婪的总和再次提供了RPG碱基。 PG和RPG碱基的伴侣表明存在RPG碱基的表征，当贪婪的总和放大时，它给出了一种结果，该结果适用于部分贪婪的基础。在本文中，我们表明确实存在这样的特征，从而积极回答了作者先前提出的问题。
An interesting result due to Dilworth et al. was that if we enlarge greedy sums by a constant factor $λ> 1$ in the condition defining the greedy property, then we obtain an equivalence of the almost greedy property, a strictly weaker property. Previously, the author of the present paper showed that enlarging greedy sums by $λ$ in the condition defining the partially greedy (PG) property also strictly weakens the property. However, enlarging greedy sums in the definition of reverse partially greedy (RPG) bases by Dilworth and Khurana again gives RPG bases. The companion of PG and RPG bases suggests the existence of a characterization of RPG bases which, when greedy sums are enlarged, gives an analog of a result that holds for partially greedy bases. In this paper, we show that such a characterization indeed exists, answering positively a question previously posed by the author.
