Mixing
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What do you call a “multi-dimensional semilattice?”
$begingroup$
Semilattices are useful for modeling certain types of systems that describe precedence or superceding. For example, in a semilattice that models "authority" systems, we can say that the join relation represents a directed acyclic graph of "chain of command."
However, suppose you want to integrate two semi-lattice that share elements. For example, suppose I have three semilattices (where each of the $lt$ operations are distinct and unique:
$$
{a, b, c} a lt_a b, a lt_a c\
{d, b, c} d lt_d b, d lt_d c\
{e, b, c} e lt_e c, e lt_e c\
$$
If I want to integrate each of the semi-lattices into the same structure, is there a name for such a structure, and how do I find out more about this?
lattice-orders
asked Jan 24 at 20:08
VermillionAzureVermillionAzure
14911
$endgroup$
add a comment |
$begingroup$
Semilattices are useful for modeling certain types of systems that describe precedence or superceding. For example, in a semilattice that models "authority" systems, we can say that the join relation represents a directed acyclic graph of "chain of command."
However, suppose you want to integrate two semi-lattice that share elements. For example, suppose I have three semilattices (where each of the $lt$ operations are distinct and unique:
$$
{a, b, c} a lt_a b, a lt_a c\
{d, b, c} d lt_d b, d lt_d c\
{e, b, c} e lt_e c, e lt_e c\
$$
If I want to integrate each of the semi-lattices into the same structure, is there a name for such a structure, and how do I find out more about this?
lattice-orders
asked Jan 24 at 20:08
VermillionAzureVermillionAzure
14911
$endgroup$
add a comment |
$begingroup$
Semilattices are useful for modeling certain types of systems that describe precedence or superceding. For example, in a semilattice that models "authority" systems, we can say that the join relation represents a directed acyclic graph of "chain of command."
However, suppose you want to integrate two semi-lattice that share elements. For example, suppose I have three semilattices (where each of the $lt$ operations are distinct and unique:
$$
{a, b, c} a lt_a b, a lt_a c\
{d, b, c} d lt_d b, d lt_d c\
{e, b, c} e lt_e c, e lt_e c\
$$
If I want to integrate each of the semi-lattices into the same structure, is there a name for such a structure, and how do I find out more about this?
lattice-orders
asked Jan 24 at 20:08
VermillionAzureVermillionAzure
14911
$endgroup$
Semilattices are useful for modeling certain types of systems that describe precedence or superceding. For example, in a semilattice that models "authority" systems, we can say that the join relation represents a directed acyclic graph of "chain of command."
However, suppose you want to integrate two semi-lattice that share elements. For example, suppose I have three semilattices (where each of the $lt$ operations are distinct and unique:
$$
{a, b, c} a lt_a b, a lt_a c\
{d, b, c} d lt_d b, d lt_d c\
{e, b, c} e lt_e c, e lt_e c\
$$
If I want to integrate each of the semi-lattices into the same structure, is there a name for such a structure, and how do I find out more about this?
lattice-orders
lattice-orders
asked Jan 24 at 20:08
VermillionAzureVermillionAzure
14911
asked Jan 24 at 20:08
VermillionAzureVermillionAzure
14911
asked Jan 24 at 20:08
VermillionAzureVermillionAzure
14911
asked Jan 24 at 20:08
VermillionAzureVermillionAzure
14911
asked Jan 24 at 20:08
VermillionAzureVermillionAzure
14911
14911
add a comment |
add a comment |
1 Answer
1
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$begingroup$
In the specific case in which you have the same underlying set, and two different orderings, each giving rise to a semilattice structure, in this paper (Journal of Algebra, 70, 78-88), Anna Romanovska and Jonathan Smith call bisemilattices to such structures.
There is a more or less extensive literature on the subject.
You might be able to overcome the problem of not having the same underlying set using some trick (like making the union of those sets and make the elements which were not to be related with others for some ordering, related in some trivial way that best fits the context).
Concerning the fact that you might have more than two semilattice structures, I would call them multi-semilattices, or some similar name, making reference to the already existing concept of bisemilattices to justify that name.
answered Jan 25 at 10:05
amrsaamrsa
3,7852618
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1 Answer
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1 Answer
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active
oldest
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$begingroup$
In the specific case in which you have the same underlying set, and two different orderings, each giving rise to a semilattice structure, in this paper (Journal of Algebra, 70, 78-88), Anna Romanovska and Jonathan Smith call bisemilattices to such structures.
There is a more or less extensive literature on the subject.
You might be able to overcome the problem of not having the same underlying set using some trick (like making the union of those sets and make the elements which were not to be related with others for some ordering, related in some trivial way that best fits the context).
Concerning the fact that you might have more than two semilattice structures, I would call them multi-semilattices, or some similar name, making reference to the already existing concept of bisemilattices to justify that name.
answered Jan 25 at 10:05
amrsaamrsa
3,7852618
$endgroup$
add a comment |
$begingroup$
In the specific case in which you have the same underlying set, and two different orderings, each giving rise to a semilattice structure, in this paper (Journal of Algebra, 70, 78-88), Anna Romanovska and Jonathan Smith call bisemilattices to such structures.
There is a more or less extensive literature on the subject.
You might be able to overcome the problem of not having the same underlying set using some trick (like making the union of those sets and make the elements which were not to be related with others for some ordering, related in some trivial way that best fits the context).
Concerning the fact that you might have more than two semilattice structures, I would call them multi-semilattices, or some similar name, making reference to the already existing concept of bisemilattices to justify that name.
answered Jan 25 at 10:05
amrsaamrsa
3,7852618
$endgroup$
add a comment |
$begingroup$
In the specific case in which you have the same underlying set, and two different orderings, each giving rise to a semilattice structure, in this paper (Journal of Algebra, 70, 78-88), Anna Romanovska and Jonathan Smith call bisemilattices to such structures.
There is a more or less extensive literature on the subject.
You might be able to overcome the problem of not having the same underlying set using some trick (like making the union of those sets and make the elements which were not to be related with others for some ordering, related in some trivial way that best fits the context).
Concerning the fact that you might have more than two semilattice structures, I would call them multi-semilattices, or some similar name, making reference to the already existing concept of bisemilattices to justify that name.
answered Jan 25 at 10:05
amrsaamrsa
3,7852618
$endgroup$
In the specific case in which you have the same underlying set, and two different orderings, each giving rise to a semilattice structure, in this paper (Journal of Algebra, 70, 78-88), Anna Romanovska and Jonathan Smith call bisemilattices to such structures.
There is a more or less extensive literature on the subject.
You might be able to overcome the problem of not having the same underlying set using some trick (like making the union of those sets and make the elements which were not to be related with others for some ordering, related in some trivial way that best fits the context).
Concerning the fact that you might have more than two semilattice structures, I would call them multi-semilattices, or some similar name, making reference to the already existing concept of bisemilattices to justify that name.
answered Jan 25 at 10:05
amrsaamrsa
3,7852618
answered Jan 25 at 10:05
amrsaamrsa
3,7852618
answered Jan 25 at 10:05
amrsaamrsa
3,7852618
answered Jan 25 at 10:05
amrsaamrsa
3,7852618
3,7852618
add a comment |
add a comment |
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