Examples by Moriyama and Takeuchi

記述

森山と竹内は2次元の擬多様体でない単体的複体でシェラブルなもの を数え挙げるという試みをし、その中でいくつもの特殊な例を発見した。

データ

[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 (これはbjorner.datと同じ。)
• v7f11.dat
• v7f12.dat
• v7f13.dat (これはnonextend.datと同じ。)

このうち、v6f9-1とv6f9-2はこの性質を持つ例の中で最小である。

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

• v6f10-1.dat(上にもある。)
• v6f10-6.dat
• v6f10-7.dat
• v7f13.dat(上にもある。)

このうち…、
[Extendably shellable but not vertex decomposable 2-dim simplicial complexes]

• v6f10-6.dat
• v6f10-7.dat

表

	vertex decomposable	extendably shellable	shellable	f-vector	h-vector	備考
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)	bjorner.datと同じ
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)	nonextend.datと同じ

参考文献

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.