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research article

Almost tiling of the Boolean lattice with copies of a poset

Tomon, Istvan  
February 16, 2018
Electronic Journal Of Combinatorics

Let P be a partially ordered set. If the Boolean lattice (2[n],⊂) can be partitioned into copies of P for some positive integer n, then P must satisfy the following two trivial conditions: (1) the size of P is a power of 2, (2) P has a unique maximal and minimal element. Resolving a conjecture of Lonc, it was shown by Gruslys, Leader and Tomon that these conditions are sufficient as well. In this paper, we show that if P only satisfies condition (2), we can still almost partition 2[n] into copies of P. We prove that if P has a unique maximal and minimal element, then there exists a constant c=c(P) such that all but at most c elements of 2[n] can be covered by disjoint copies of P.

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Type
research article
DOI
10.37236/6636
Web of Science ID

WOS:000432156600012

Author(s)
Tomon, Istvan  
Date Issued

2018-02-16

Publisher

ELECTRONIC JOURNAL OF COMBINATORICS

Published in
Electronic Journal Of Combinatorics
Volume

25

Issue

1

Article Number

P1.38

Subjects

Mathematics, Applied

•

Mathematics

•

tiling

•

boolean lattice

•

poset

Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
DCG  
Available on Infoscience
November 14, 2018
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/151431
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