To show that detM
is non-zero, we can show that its 2-adic valuation is nonzero.
I think the last word in that sentence should be "finite"?
Also do I understand correctly that "face" means "maximal line segment"? (I see some other comments discussing this and concluding that "face" means "edge", but to me, an "edge" doesn't permit "intermediate" vertices.)
Also do I understand correctly that "face" means "maximal line segment"?
In the statement of Sperners lemma this seems to be how he means it. You have a triangle who's faces have been subdivided. The face he is referring to is the face before subdivision I think.
This lines up with the usual statement I'm familiar with for Sperners lemma which involves triangulating an n-simplex.
Comments
I think the last word in that sentence should be "finite"?
Also do I understand correctly that "face" means "maximal line segment"? (I see some other comments discussing this and concluding that "face" means "edge", but to me, an "edge" doesn't permit "intermediate" vertices.)
In the statement of Sperners lemma this seems to be how he means it. You have a triangle who's faces have been subdivided. The face he is referring to is the face before subdivision I think.
This lines up with the usual statement I'm familiar with for Sperners lemma which involves triangulating an n-simplex.
Yep, you're right on both counts; I've updated the page with those corrections. Thanks!