A family of asymptotically \(e(n-1)!\) polynomial orders of \(N^n\)
type: Item
instance of: scholarly article
title: A family of asymptotically \(e(n-1)!\) polynomial orders of \(N^n\)
zbMATH Open document ID: 0948.06001
DOI: 10.1023/A:1006329224202
author: Luis B. Morales
author: Juan H. Arredondo R.
published in: Order
publication date: 2000-11-14T00:00:00Z
review text: Denote by \(N^n\) the \(n\)-sequences of non-negative integers. If \({\mathbf x}\in N^n\) then \(s({\mathbf x})=x_1+\cdots+x_n.\) An order of \(N^n\) is a bijection \(\alpha: N^n \rightarrow N.\) Two orders are equivalent if they differ only by a permutation of their arguments. Finally an order \(\alpha\) is diagonal if \(\alpha({\mathbf x})< \alpha({\mathbf y})\) whenever \(s({\mathbf x})< s({\mathbf y}).\) There is a long quest for larger and larger families or non-isomorphic diagonal or nondiagonal orders. This paper constructs a new family of nondiagonal orders, using an earlier diagonal order construction of Sanchez, highly improving any earlier order families.
Mathematics Subject Classification ID: 06A06
Mathematics Subject Classification ID: 68R05
zbMATH DE Number: 1463102
zbMATH Keywords: diagonal orders
zbMATH Keywords: plane trees
zbMATH Keywords: polynomial orders
zbMATH Keywords: nondiagonal orders
reviewed by: Péter L. Erdős
MaRDI profile type: Publication
full work available at URL: a:1006329224202
OpenAlex ID: W56550333
description: scientific article; zbMATH DE number 1463102