Forbidden Families of Geometric Permutations in R
نویسنده
چکیده
A geometric permutation induced by a transversal line of a finite family F of disjoint convex sets in Rd is the order in which the transversal meets the members of the family. We prove that for each natural k, each family of k permutations is realizable (as a family of geometric permutations of some F ) in Rd for d ≥ 2k − 1, but there is a family of k permutations which is non-realizable in Rd for d ≤ 2k − 2.
منابع مشابه
The triples of geometric permutations for families of disjoint translates
A line meeting a family of pairwise disjoint convex sets induces two permutations of the sets. This pair of permutations is called a geometric permutation. We characterize the possible triples of geometric permutations for a family of disjoint translates in the plane. Together with earlier studies of geometric permutations this provides a complete characterization of realizable geometric permut...
متن کاملSorting classes – Extended Abstract
Weak and strong sorting classes are pattern-closed classes that are also closed downwards under the weak and strong orders on permutations. They are studied using partial orders that capture both the subpermutation order and the weak or strong order. In both cases they can be characterised by forbidden permutations in the appropriate order. The connection with the corresponding forbidden permut...
متن کاملPermutation Classes of Polynomial Growth
A pattern class is a set of permutations closed under the formation of subpermutations. Such classes can be characterized as those permutations not involving a particular set of forbidden permutations. A simple collection of necessary and sufficient conditions on sets of forbidden permutations which ensure that the associated pattern class is of polynomial growth is determined. A catalogue all ...
متن کاملDyck paths and restricted permutations
This paper is devoted to characterize permutations with forbidden patterns by using canonical reduced decompositions, which leads to bijections between Dyck paths and Sn(321) and Sn(231), respectively. We also discuss permutations in Sn avoiding two patterns, one of length 3 and the other of length k. These permutations produce a kind of discrete continuity between the Motzkin and the Catalan n...
متن کاملOn basic forbidden patterns of functions
The allowed patterns of a map on a one-dimensional interval are those permutations that are realized by the relative order of the elements in its orbits. The set of allowed patterns is completely determined by the minimal patterns that are not allowed. These are called basic forbidden patterns. In this paper we study basic forbidden patterns of several functions. We show that the logistic map L...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005