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Gerry Myerson
Gerry Myerson
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convexe convex hull of the set of permutationpermutations with one cycle

is there a way to describe the convexeconvex hull of the set of permutation matrices with exactly one non-trivial cycle?

or maybe I should ask for the convexeconvex hull of cycle matrices :

let $(i_{1},..,i_{k})$ be a cycle then $A$ is a cycle matrix if the entries $(i_{1},i_{2})$ ...$(i_{k},i_{1})$ are $1/k$, and all the others are 0. (it seems to me that this convex hull is the set of non-negative matrices of entries sum equal to 1)

convexe hull of the set of permutation with one cycle

is there a way to describe the convexe hull of the set of permutation matrices with exactly one non-trivial cycle?

or maybe I should ask for the convexe hull of cycle matrices :

let $(i_{1},..,i_{k})$ be a cycle then $A$ is a cycle matrix if the entries $(i_{1},i_{2})$ ...$(i_{k},i_{1})$ are $1/k$, and all the others are 0. (it seems to me that this convex hull is the set of non-negative matrices of entries sum equal to 1)

convex hull of the set of permutations with one cycle

is there a way to describe the convex hull of the set of permutation matrices with exactly one non-trivial cycle?

or maybe I should ask for the convex hull of cycle matrices :

let $(i_{1},..,i_{k})$ be a cycle then $A$ is a cycle matrix if the entries $(i_{1},i_{2})$ ...$(i_{k},i_{1})$ are $1/k$, and all the others are 0. (it seems to me that this convex hull is the set of non-negative matrices of entries sum equal to 1)

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zack
zack
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convexe hull of the set of permutation with one cycle

is there a way to describe the convexe hull of the set of permutation matrices with exactly one non-trivial cycle?

or maybe I should ask for the convexe hull of cycle matrices :

let $(i_{1},..,i_{k})$ be a cycle then $A$ is a cycle matrix if the entries $(i_{1},i_{2})$ ...$(i_{k},i_{1})$ are $1/k$, and all the others are 0. (it seems to me that this convex hull is the set of non-negative matrices of entries sum equal to 1)