Dimension Preserving Contractions and a Finite List of 3-Irreducible Posets

被引：1
作者：
Streib, Noah [1 ]
机构：
[1] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA
来源：
ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS | 2012年 / 29卷 / 01期
关键词：
Poset; Dimension; 3-Irreducible; Contraction; PARTIALLY ORDERED SETS; LATTICES; GRAPHS;
D O I：
10.1007/s11083-011-9204-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper introduces new poset operations-dimension-preserving contractions. These contractions are used to change a poset into a similar, but simpler, poset with the same dimension. In particular, they can be used to turn the well-known infinite list of 3-irreducible posets into seventeen 3-irreducible, noncontractible posets (up to duality).
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收藏
页码：165 / 176
页数：12
相关论文
共 12 条
[1]   The maximum number of edges in a graph of bounded dimension, with applications to ring theory [J].
Agnarsson, G ;
Felsner, S ;
Trotter, WT .
DISCRETE MATHEMATICS, 1999, 201 (1-3) :5-19
[2]  
[Anonymous], 1992, Combinatorics and Partially Ordered Sets: Dimension Theory
[3]   THE ORDER DIMENSION OF CONVEX POLYTOPES [J].
BRIGHTWELL, G ;
TROTTER, WT .
SIAM JOURNAL ON DISCRETE MATHEMATICS, 1993, 6 (02) :230-245
[4]   The order dimension of planar maps [J].
Brightwell, GR ;
Trotter, WT .
SIAM JOURNAL ON DISCRETE MATHEMATICS, 1997, 10 (04) :515-528
[5]   Partially ordered sets [J].
Dushnik, B ;
Miller, EW .
AMERICAN JOURNAL OF MATHEMATICS, 1941, 63 :600-610
[6]   TRANSITIV ORIENTIERBARE GRAPHEN [J].
GALLAI, T .
ACTA MATHEMATICA ACADEMIAE SCIENTIARUM HUNGARICAE, 1967, 18 (1-2) :25-&
[7]  
Hegde Rajneesh., 2007, P EUROPEAN C COMBINA, P435, DOI DOI 10.1016/J.ENDM.2007.07.084
[8]   PLANAR LATTICES [J].
KELLY, D ;
RIVAL, I .
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1975, 27 (03) :636-665
[9]  
Kelly D., 1977, CAN J MATH, V35, P367
[10]   PLANAR GRAPHS AND POSET DIMENSION [J].
SCHNYDER, W .
ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, 1989, 5 (04) :323-343
12