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Non-constructible Complexes and the Bridge Index

✍ Scribed by Richard Ehrenborg; Masahiro Hachimori

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
210 KB
Volume
22
Category
Article
ISSN
0195-6698

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✦ Synopsis

We show that if a three-dimensional polytopal complex has a knot in its 1-skeleton, where the bridge index of the knot is larger than the number of edges of the knot, then the complex is not constructible, and hence, not shellable. As an application we settle a conjecture of Hetyei concerning the shellability of cubical barycentric subdivisions of 3-spheres. We also obtain similar bounds concluding that a 3-sphere or 3-ball is non-shellable or not vertex decomposable. These two last bounds are sharp.

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Treatment of (CO) 5 W=C(NMe 2 )CH=CH-Ar-(OH)(H)CΟ΅CH (1a-b) [a: -Ar-=1,4-C 6 H 4 -; b: -Ar-= 2,5-C 4 H 2 S-] with W(CO) 5 (THF) in methanol yields the nonsymmetrical bis(alkenylcarbene)-bridged ditungsten complexes (CO) 5 W= C(NMe 2 )CH=CH-Ar-CH=CH(OMe)C=W(CO) 5 (3a-b). Similarly, the symmetrical bis