Number of faces of dimension p of simplex
$begingroup$
How can I prove that the number of faces of dimension p of an an n-dimensions simplex is represented by the binomial coefficient below?
${n+1}choose{p+1}$
geometry simplex
asked Jan 14 at 14:20
mgrmgr
246
$endgroup$
add a comment |
$begingroup$
How can I prove that the number of faces of dimension p of an an n-dimensions simplex is represented by the binomial coefficient below?
${n+1}choose{p+1}$
geometry simplex
asked Jan 14 at 14:20
mgrmgr
246
$endgroup$
add a comment |
$begingroup$
How can I prove that the number of faces of dimension p of an an n-dimensions simplex is represented by the binomial coefficient below?
${n+1}choose{p+1}$
geometry simplex
asked Jan 14 at 14:20
mgrmgr
246
$endgroup$
How can I prove that the number of faces of dimension p of an an n-dimensions simplex is represented by the binomial coefficient below?
${n+1}choose{p+1}$
geometry simplex
geometry simplex
asked Jan 14 at 14:20
mgrmgr
246
asked Jan 14 at 14:20
mgrmgr
246
asked Jan 14 at 14:20
mgrmgr
246
asked Jan 14 at 14:20
mgrmgr
246
asked Jan 14 at 14:20
mgrmgr
246
246
add a comment |
add a comment |
1 Answer
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$begingroup$
an $n$-dimensional simplex is made up by $(n+1)$ vertices. any $(p+1)$ vertices will make up one $p$-dimensional face. (it takes two vertices to create an edge, three to make a triangle, 4 for a tetrahedron, etc...) in fact, there is precisely a $p$-simplex between any $(p+1)$ vertices, because simplexes are complete graphs.
answered Jan 14 at 14:51
Zachary HunterZachary Hunter
57611
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1 Answer
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1 Answer
1
active
oldest
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active
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active
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votes
$begingroup$
an $n$-dimensional simplex is made up by $(n+1)$ vertices. any $(p+1)$ vertices will make up one $p$-dimensional face. (it takes two vertices to create an edge, three to make a triangle, 4 for a tetrahedron, etc...) in fact, there is precisely a $p$-simplex between any $(p+1)$ vertices, because simplexes are complete graphs.
answered Jan 14 at 14:51
Zachary HunterZachary Hunter
57611
$endgroup$
add a comment |
$begingroup$
an $n$-dimensional simplex is made up by $(n+1)$ vertices. any $(p+1)$ vertices will make up one $p$-dimensional face. (it takes two vertices to create an edge, three to make a triangle, 4 for a tetrahedron, etc...) in fact, there is precisely a $p$-simplex between any $(p+1)$ vertices, because simplexes are complete graphs.
answered Jan 14 at 14:51
Zachary HunterZachary Hunter
57611
$endgroup$
add a comment |
$begingroup$
an $n$-dimensional simplex is made up by $(n+1)$ vertices. any $(p+1)$ vertices will make up one $p$-dimensional face. (it takes two vertices to create an edge, three to make a triangle, 4 for a tetrahedron, etc...) in fact, there is precisely a $p$-simplex between any $(p+1)$ vertices, because simplexes are complete graphs.
answered Jan 14 at 14:51
Zachary HunterZachary Hunter
57611
$endgroup$
an $n$-dimensional simplex is made up by $(n+1)$ vertices. any $(p+1)$ vertices will make up one $p$-dimensional face. (it takes two vertices to create an edge, three to make a triangle, 4 for a tetrahedron, etc...) in fact, there is precisely a $p$-simplex between any $(p+1)$ vertices, because simplexes are complete graphs.
answered Jan 14 at 14:51
Zachary HunterZachary Hunter
57611
answered Jan 14 at 14:51
Zachary HunterZachary Hunter
57611
answered Jan 14 at 14:51
Zachary HunterZachary Hunter
57611
answered Jan 14 at 14:51
Zachary HunterZachary Hunter
57611
57611
add a comment |
add a comment |
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