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MR1662257 (2000k:57023) 57Q05 (20B25 20C30)
Kozlov, Dmitry N. Collapsibility of $\Delta(\Pi\sb n)/\scr S\sb n$ and some related CW complexes. Proc. Amer. Math. Soc. 128 (2000), no. 8, 2253–2259.
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