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An improvement on a spernerity proof of Horrocks

Szu-En Cheng, Ko-Wei Lih
2001 Theoretical Computer Science  
In Horrocks' proof (Horrocks, European Journal of Combinatorics 20 (1999) 131-148) of Lih's conjecture about the Spernerity of ÿlters in a Boolean algebra generated by 2-subsets, there are 116 exceptional  ...  The details of the analysis could not be published in its entirety. In this paper we carry Horrocks' method much further to reduce the exceptional cases to a manageable number.  ...  Horrocks [2] gave an a rmative solution for the case t = 2. Horrocks ÿrst transformed the problem into an equivalent form in terms of graphs.  ... 
doi:10.1016/s0304-3975(00)00255-3 fatcat:z27rpgy5qfhjvhe6ahu4v6x27a

Author index volume 263 (2001)

2001 Theoretical Computer Science  
Lih, An improvement on a spernerity proof of Horrocks (1}2) 355}377 CleH menc7 on, H., see C. Indermitte (1}2) 263}274 Damiand, G., M. Habib and C.  ...  CleH menc7 on, Voronoi diagrams on piecewise #at surfaces and an application to biological growth (1}2) 263}274 KaH rolyi, G. and V.  ... 
doi:10.1016/s0304-3975(01)00283-3 fatcat:xv3da2ixwzf4pfp47jgune5zg4

Page 7844 of Mathematical Reviews Vol. , Issue 2002K [page]

2002 Mathematical Reviews  
improvement on a Spernerity proof of Horrocks.  ...  Assume p pebbles are distributed onto the vertices of a graph G, and define a pebbling move to be the removal of two pebbles from one vertex and the subsequent placement of one pebble at an adjacent vertex  ... 

Methods for nesting rank 3 normalized matching rank-unimodal posets

Tim Hsu, Mark J. Logan, Shahriar Shahriari
2009 Discrete Mathematics  
Anderson and Griggs proved independently that a rank-symmetric-unimodal normalized matching (NM) poset possesses a nested chain decomposition (or nesting), and Griggs later conjectured that this result  ...  We give several methods for constructing nestings of rank-unimodal NM posets of rank 3, which together produce substantial progress towards the rank 3 case of the Griggs nesting conjecture.  ...  Acknowledgements We thank Katherine Shelley Nolan for the use of material in her master's thesis [28] (later incorporated into [26] ) that greatly helped to improve the exposition in this paper.  ... 
doi:10.1016/j.disc.2008.07.013 fatcat:wqkz2rffdrbxnmmd5uyb5e6gza

Page 200 of Mathematical Reviews Vol. , Issue Subject Index [page]

Mathematical Reviews  
English and Slovenian summaries) Britz, Thomas (with Fomin, Sergey) Finite posets and Ferrers shapes. 2002c:05162 Cheng, Szu-En (with Lih, Ko-Wei) An improvement on a Spernerity proof of Horrocks.  ...  (English summary) 2002a:54014 Harzheim, Egbert On the Dedekind-MacNeille closure of an ordered set and a theorem of Novak.  ... 

Page 330 of Mathematical Reviews Vol. , Issue Author Index [page]

Mathematical Reviews  
(Summary) 2002m:34051 34C10 Cheng, Szu-En (with Lih, Ko-Wei) An improvement on a Spernerity proof of Horrocks. (English summary) Combinatorics and computer science (Palaiseau, 1997). Theoret. Comput.  ...  Systems Appl. 9 (2000), no. 3, 457-461. 39A10 — (with Si, Jian-Guo; Zhang, Wei Nian) Continuous solutions of an iterative functional inequality on compact interval.  ... 

The Distributive, Graded Lattice of EL Concept Descriptions and its Neighborhood Relation (Extended Version) [article]

Francesco Kriegel
2019 arXiv   pre-print
In particular, this implies the existence of a rank function as well as the existence of a distance function.  ...  For the description logic EL, we consider the neighborhood relation which is induced by the subsumption order, and we show that the corresponding lattice of EL concept descriptions is distributive, modular  ...  well as for providing comments that helped to improve the quality of this document.  ... 
arXiv:1901.05919v1 fatcat:nspj4aczdfb2xekvadmgma4v3i

Page 1152 of Mathematical Reviews Vol. , Issue Author Index [page]

Mathematical Reviews  
(Summary) 2002a:05152 05C38 — (with Cheng, Szu-En) An improvement on a Spernerity proof of Horrocks. (English summary) Combinatorics and computer science (Palaiseau, 1997). Theoret. Comput.  ...  Notes of an old graduate student. The many faces of the superworld, 25-31, World Sci. Publishing, River Edge, NJ, 2000. (see 2002j:81002) 01A70 — (with Gol'fand, Yu. A.)  ...