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Jul
2
awarded  Curious
Apr
30
awarded  Yearling
Jun
6
comment How many cuts does it take to remove any $n$ vertices from an $m$-dimensional hypercube?
Ahh yup - overlooked the obvious - thanks
Jun
6
revised How many cuts does it take to remove any $n$ vertices from an $m$-dimensional hypercube?
added 8 characters in body; deleted 37 characters in body
Jun
6
awarded  Commentator
Jun
6
comment How many cuts does it take to remove any $n$ vertices from an $m$-dimensional hypercube?
@andewsalmon - I'm interested in the minimum number to cut off any $n$ given vertices, meaning I allow for the case of not being adjacent. Sure, for adjacent cases you may use less cuts, but I need to be able to cut off any $n$ given vertices in $C(m,n)$ cuts.
Jun
6
asked How many cuts does it take to remove any $n$ vertices from an $m$-dimensional hypercube?
Jun
5
revised Characterisation of linearly separable points of a hypercube
added 11 characters in body
Jun
5
comment Characterisation of linearly separable points of a hypercube
@AsalBeagDubh - thanks, sounds like that might be what I want, but what is $p_i - p_0$?
Jun
5
asked Characterisation of linearly separable points of a hypercube
Jun
5
awarded  Nice Question
Jun
4
comment How many hyperplanes does it take to separate $n$ points in $\mathbb{R}^m$?
Yes, as in the notion of general position. Clearly, it requires more lines to separate collinear points. In particular, points in general position in $\mathbb{R^{m-1}}$ when viewed in $\mathbb{R^{m}}$ lie on a plane, which is no longer in general position (and is removed from consideration). Hence @AlexRavsky's deduction $P(m,n)≤P(m−1,n)$.
Jun
4
comment How to express exclusive intersections?
I think it might be $M(S) = \bigcap S \setminus \ldots$ though. Thanks
Jun
4
accepted How to express exclusive intersections?
Jun
4
comment How many hyperplanes does it take to separate $n$ points in $\mathbb{R}^m$?
Just to be clear, I presume that's $\log$ base 2?
Jun
4
asked How many hyperplanes does it take to separate $n$ points in $\mathbb{R}^m$?
Jun
4
revised Can $n$ hyperplanes separate any $\sum_{k = 0}^{m} \binom{n}{k}$ points in $\mathbb{R}^m$?
deleted 15 characters in body; edited title; added 11 characters in body; edited title; edited title; edited title
Jun
4
accepted Can $n$ hyperplanes separate any $\sum_{k = 0}^{m} \binom{n}{k}$ points in $\mathbb{R}^m$?
Jun
3
revised Can $n$ hyperplanes separate any $\sum_{k = 0}^{m} \binom{n}{k}$ points in $\mathbb{R}^m$?
deleted 16 characters in body
Jun
3
comment Can $n$ hyperplanes separate any $\sum_{k = 0}^{m} \binom{n}{k}$ points in $\mathbb{R}^m$?
Whoops - thanks guys. Fixed question