Examples by Moriyama and Takeuchi

Description

Moriyama & Takeuchi attempted to enumerate all shellable non-pseudomanifold 2-dim simplicial complexes, and their enumeration found out many interesting examples.

Datum

[Shellable but not extendably shellable 2-dim simplicial complexes.]

• v6f9-1.dat
• v6f9-2.dat
• v6f10-1.dat
• v6f10-2.dat
• v6f10-3.dat
• v6f10-4.dat
• v6f10-5.dat
• v6f11-1.dat
• v6f11-2.dat
• v6f11-3.dat (The same as bjorner.dat.)
• v7f11.dat
• v7f12.dat
• v7f13.dat (The same as nonextend.dat.)

Among these, v6f9-1 and v6f9-2 are the minimum example with this property.

[Shellable but not vertex decomposable 2-dim simplicial complexes]

• v6f10-1.dat (Also listed above.)
• v6f10-6.dat
• v6f10-7.dat
• v7f13.dat (Also listed above.)

Among these,
[Extendably shellable but not vertex decomposable 2-dim simplicial complexes]

• v6f10-6.dat
• v6f10-7.dat

Some table

	vertex decomposable	extendably shellable	shellable	f-vector	h-vector	Comments
v6f9-1.dat		no	yes	(1,6,14,9)	(1,3,5,0)
v6f9-2.dat		no	yes	(1,6,14,9)	(1,3,5,0)
v6f10-1.dat	no	no	yes	(1,6,15,10)	(1,3,6,0)
v6f10-2.dat		no	yes	(1,6,15,10)	(1,3,6,0)
v6f10-3.dat		no	yes	(1,6,15,10)	(1,3,6,0)
v6f10-4.dat		no	yes	(1,6,15,10)	(1,3,6,0)
v6f10-5.dat		no	yes	(1,6,15,10)	(1,3,6,0)
v6f10-6.dat	no	yes	yes	(1,6,15,10)	(1,3,6,0)
v6f10-7.dat	no	yes	yes	(1,6,15,10)	(1,3,6,0)
v6f11-1.dat		no	yes	(1,6,15,11)	(1,3,6,1)
v6f11-2.dat		no	yes	(1,6,15,11)	(1,3,6,1)
v6f11-3.dat		no	yes	(1,6,15,11)	(1,3,6,1)	The same as bjorner.dat.
v7f11.dat		no	yes	(1,7,17,11)	(1,4,6,0)
v7f12.dat		no	yes	(1,7,18,12)	(1,4,7,0)
v7f13.dat	no	no	yes	(1,7,19,13)	(1,4,8,0)	The same as nonextend.dat.

References

Sonoko Moriyama, Extendable shellability in dimension two, Bachelor's thesis.

Sonoko Moriyama and Fumihiko Takeuchi, Incremental construction properties in dimension two --- shellability, extendable shellability and vertex decomposability, preprint.