Strictly Order-Preserving Maps into Z, II. A 1979 Problem of Erné

被引：0

作者：

Jonathan David Farley

Bernd S. W. Schröder

机构：

[1] Vanderbilt University,Department of Mathematics

[2] Mathematical Sciences Research Institute,Program of Mathematics and Statistics

[3] Louisiana Tech University,Department of Mathematics

[4] Hampton University,undefined

来源：

Order | 2001年 / 18卷

关键词：

chain; lattice; (partially) ordered set; (strictly) order-preserving map;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

A lattice L is constructed with the property that every interval has finite height, but there exists no strictly order-preserving map from L to Z. A 1979 problem of Erné (posed at the 1981 Banff Conference on Ordered Sets) is thus solved. It is also shown that if a poset P has no uncountable antichains, then it admits a strictly order-preserving map into Z if and only if every interval has finite height.

引用

页码：381 / 385

页数：4

共 50 条

[21] The finite basis problem for the semigroups of order-preserving mappings
Vernitskii, AS
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1999, 129 : 641 - 647
[22] ON WEAKLY GRADED POSETS OF ORDER-PRESERVING MAPS UNDER THE NATURAL PARTIAL ORDER
Jitjankarn, Phichet
COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY, 2020, 35 (02): : 347 - 358
[23] Upper and lower bounds for the iterates of order-preserving homogeneous maps on cones
Chodrow, Philip
Franks, Cole
Lins, Brian
LINEAR ALGEBRA AND ITS APPLICATIONS, 2013, 439 (04) : 999 - 1005
[24] Abelian Kernels of Monoids of Order-preserving Maps and of Some of Its Extensions
Manuel Delgado
Vítor H. Fernandes
Semigroup Forum, 2004, 68 : 335 - 356
[25] Eigenfunctionals of Homogeneous Order-Preserving Maps with Applications to Sexually Reproducing Populations
Thieme, Horst R.
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2016, 28 (3-4) : 1115 - 1144
[26] Cometic functors and representing order-preserving maps by principal lattice congruences
Czedli, Gabor
ALGEBRA UNIVERSALIS, 2018, 79 (03)
[27] Abelian kernels of monoids of order-preserving maps and of some of its extensions
Delgado, M
Fernandes, VH
SEMIGROUP FORUM, 2004, 68 (03) : 335 - 356
[28] Cometic functors and representing order-preserving maps by principal lattice congruences
Gábor Czédli
Algebra universalis, 2018, 79
[29] Eigenfunctionals of Homogeneous Order-Preserving Maps with Applications to Sexually Reproducing Populations
Horst R. Thieme
Journal of Dynamics and Differential Equations, 2016, 28 : 1115 - 1144
[30] On the Deep Order-Preserving Submatrix Problem: A Best Effort Approach
Gao, Byron J.
Griffith, Obi L.
Ester, Martin
Xiong, Hui
Zhao, Qiang
Jones, Steven J. M.
IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING, 2012, 24 (02) : 309 - 325

← 1 2 3 4 5 →