منابع مشابه
Uniqueness in the Left Division of Order Types
Proof. In [4] it was shown that ps<pt for any two positive integers 5 and / for which s<t. Hence the lemma is true if 7 and 5 are each integers. Since, for 5 finite, ps<p(s + l) ^uo)^p(oo*+oj) and ps<p(s + l) ^pco*^p(co*+o}), it follows that the lemma is true if one of the elements 7 or 5 is finite, and the other is not. Suppose that pu and pu* are demonstrated to be incomparable order types.2 ...
متن کاملOrder on Order Types
Given P and P ′, equally sized planar point sets in general position, we call a bijection from P to P ′ crossing-preserving if crossings of connecting segments in P are preserved in P ′ (extra crossings may occur in P ′). If such a mapping exists, we say that P ′ crossing-dominates P , and if such a mapping exists in both directions, P and P ′ are called crossing-equivalent. The relation is tra...
متن کاملLimits of Order Types
The notion of limits of dense graphs was invented, among other reasons, to attack problems in extremal graph theory. It is straightforward to define limits of order types in analogy with limits of graphs, and this paper examines how to adapt to this setting two approaches developed to study limits of dense graphs. We first consider flag algebras, which were used to open various questions on gra...
متن کاملOrder-Sorted Inductive Types
System F ! is an extension of system F ! with subtyping and bounded quantiication. Order-sorted algebra is an extension of many-sorted algebra with overloading and subtyping. We combine both formalisms to obtain IF ! , a higher-order typed-calculus with subtyping, bounded quan-tiication and order-sorted inductive types, i.e. data types with built-in subtyping and overloading. Moreover we show t...
متن کاملOrder Types of Convex Bodies
We prove a Hadwiger transversal type result, characterizing convex position on a family of non-crossing convex bodies in the plane. This theorem suggests a definition for the order type of a family of convex bodies, generalizing the usual definition of order type for point sets. This order type turns out to be an oriented matroid. We also give new upper bounds on the Erdős-Szekeres theorem in t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2020
ISSN: 0166-8641
DOI: 10.1016/j.topol.2020.107338