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0

$begingroup$

Consider a 'row' which can be in one of $n$ states. I have an $n times n$ matrix $M$ such that $M(i,j)$ gives the interaction energy between a lower row in state $i$ and a row in state $j$ placed directly above it. I now want to stack infinitely many rows on top of each other in such a way that minimizes the total interaction energy. Is there a way to determine the sequence of states?

For example, if there were only 4 stacked rows, in states 13, 71, 49 and 52, the total energy would be $M(13,71) + M(71,49) + M(49,52)$.

matrices

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fluteflute

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0

$begingroup$

Consider a 'row' which can be in one of $n$ states. I have an $n times n$ matrix $M$ such that $M(i,j)$ gives the interaction energy between a lower row in state $i$ and a row in state $j$ placed directly above it. I now want to stack infinitely many rows on top of each other in such a way that minimizes the total interaction energy. Is there a way to determine the sequence of states?

For example, if there were only 4 stacked rows, in states 13, 71, 49 and 52, the total energy would be $M(13,71) + M(71,49) + M(49,52)$.

matrices

share|cite|improve this question

edited 2 days ago

flute

asked 2 days ago

fluteflute

12

New contributor

flute is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

add a comment | 

$begingroup$

Consider a 'row' which can be in one of $n$ states. I have an $n times n$ matrix $M$ such that $M(i,j)$ gives the interaction energy between a lower row in state $i$ and a row in state $j$ placed directly above it. I now want to stack infinitely many rows on top of each other in such a way that minimizes the total interaction energy. Is there a way to determine the sequence of states?

For example, if there were only 4 stacked rows, in states 13, 71, 49 and 52, the total energy would be $M(13,71) + M(71,49) + M(49,52)$.

matrices

share|cite|improve this question

edited 2 days ago

flute

asked 2 days ago

fluteflute

12

New contributor

flute is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

share|cite|improve this question

edited 2 days ago

flute

asked 2 days ago

fluteflute

12

New contributor

flute is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share|cite|improve this question

edited 2 days ago

flute

asked 2 days ago

fluteflute

12

New contributor

flute is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked 2 days ago

fluteflute

12

New contributor

flute is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked 2 days ago

fluteflute

12