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• Ordered set  (2)
• partition  (1)
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• 1
Electronic Resource
Springer
Order 11 (1994), S. 149-158
ISSN: 1572-9273
Keywords: 06A07 ; Ordered set ; antichain ; fibre
Source: Springer Online Journal Archives 1860-2000
Topics: Mathematics
Notes: Abstract We show that in an ordered setP of width 3 there always exists a fibre (i.e., a subset intersecting each maximal nontrivial antichain) of size at most 11/18|P|. This improves previously known results.
Type of Medium: Electronic Resource
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• 2
Electronic Resource
Springer
Order 11 (1994), S. 343-351
ISSN: 1572-9273
Keywords: 06A07 ; 68R10 ; Ordered set ; chain partition ; computational complexity
Source: Springer Online Journal Archives 1860-2000
Topics: Mathematics
Notes: Abstract Lete be a fixed family of chains, i.e.e $$\subseteq \{ \underset{\raise0.3em\hbox{\smash{\scriptscriptstyle\thicksim}}}{1} ,\underset{\raise0.3em\hbox{\smash{\scriptscriptstyle\thicksim}}}{2} ,\underset{\raise0.3em\hbox{\smash{\scriptscriptstyle\thicksim}}}{3} ,...\}$$ . Ae-partition of an ordered setP=(X, ⩽) is a partition ofX into subsets inducing chains isomorphic to the members ofe. In this paper we classify according to the computational complexity problems of existence of ae-partition ofP.
Type of Medium: Electronic Resource
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• 3
Electronic Resource
Springer
Order 8 (1991), S. 17-27
ISSN: 1572-9273
Keywords: 06A23 ; Boolean lattice ; partition ; chain
Source: Springer Online Journal Archives 1860-2000
Topics: Mathematics
Notes: Abstract Let n and c be positive integers. We show that if n is sufficiently large given c then the Boolean lattice consisting of all subsets of an n-element set can be partitioned into chains of size c except for at most c — 1 elements which also form a chain. This settles a conjecture of Griggs.
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