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Semigroup from posets

asked 2022-01-27 20:38:48 +0200

klaaa gravatar image

Let $P$ be a finite poset (we can assume it is connected). Then on the set of intervals $Int(P)$ there is a semigroup structure given by the multiplication: $[a,b][c,d]=[a,d] if b=c$ and $[a,b][c,d]=0$, else.

Question: Is there an easy way to obtain for a given poset $P$, this semigroup in Sage?

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At very least it can be done like in this answer

Max Alekseyev gravatar imageMax Alekseyev ( 2022-01-27 22:10:08 +0200 )edit

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answered 2022-01-27 22:03:58 +0200

tkarn gravatar image

You could try creating creating a finite-dimensional algebra with basis specified by the relation iterator in the poset.

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Asked: 2022-01-27 20:38:48 +0200

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Last updated: Jan 27 '22