Primary source for definitions re partitions, coarsest common refinement, join/meet etc.?
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As much as I do appreciate the contributions on m.se, I need to be able to cite a primary source for definitions related to partitions, e.g., what a refinement/coarsening is, coarsest common refinement, etc.
There must exist a text that covers it, because this question, "refinement of partition clarification," quotes from one but references it only as "my book."
I run across these concepts in game theory, discussions of common knowledge, etc., but--as is typically the case when math is discussed in an allied field--the requisite concepts/theorems are exploited but without citation.
I'm not sure exactly what field covers this. I've heard set theory conjectured and then rebutted.
(I've seen "join" equated to coarsest common refinement, suggesting this might be covered by lattice theory, but when I browse tables of contents for lattice-theory books, they don't obviously cover these partition concepts.)
From game theory, I'm all too familiar with "folk knowledge" that is passed down from generation to generation without being systematically codified. I'm hoping that these concepts have escaped that category.
(If either of my tags is off-target, feel free to delete if you have the reputation to do so.)
elementary-set-theory game-theory lattice-orders
asked Dec 24 '18 at 23:59
Jim RatliffJim Ratliff
1011
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add a comment |
$begingroup$
As much as I do appreciate the contributions on m.se, I need to be able to cite a primary source for definitions related to partitions, e.g., what a refinement/coarsening is, coarsest common refinement, etc.
There must exist a text that covers it, because this question, "refinement of partition clarification," quotes from one but references it only as "my book."
I run across these concepts in game theory, discussions of common knowledge, etc., but--as is typically the case when math is discussed in an allied field--the requisite concepts/theorems are exploited but without citation.
I'm not sure exactly what field covers this. I've heard set theory conjectured and then rebutted.
(I've seen "join" equated to coarsest common refinement, suggesting this might be covered by lattice theory, but when I browse tables of contents for lattice-theory books, they don't obviously cover these partition concepts.)
From game theory, I'm all too familiar with "folk knowledge" that is passed down from generation to generation without being systematically codified. I'm hoping that these concepts have escaped that category.
(If either of my tags is off-target, feel free to delete if you have the reputation to do so.)
elementary-set-theory game-theory lattice-orders
asked Dec 24 '18 at 23:59
Jim RatliffJim Ratliff
1011
$endgroup$
1
$begingroup$
The proper field is combinatorics. The partitions form a lattice (whether you mean integer partitions or set partitions) but it's a very special one, not a central object of study in massive theory.
$endgroup$
– Matt Samuel
Dec 25 '18 at 11:25
add a comment |
$begingroup$
As much as I do appreciate the contributions on m.se, I need to be able to cite a primary source for definitions related to partitions, e.g., what a refinement/coarsening is, coarsest common refinement, etc.
There must exist a text that covers it, because this question, "refinement of partition clarification," quotes from one but references it only as "my book."
I run across these concepts in game theory, discussions of common knowledge, etc., but--as is typically the case when math is discussed in an allied field--the requisite concepts/theorems are exploited but without citation.
I'm not sure exactly what field covers this. I've heard set theory conjectured and then rebutted.
(I've seen "join" equated to coarsest common refinement, suggesting this might be covered by lattice theory, but when I browse tables of contents for lattice-theory books, they don't obviously cover these partition concepts.)
From game theory, I'm all too familiar with "folk knowledge" that is passed down from generation to generation without being systematically codified. I'm hoping that these concepts have escaped that category.
(If either of my tags is off-target, feel free to delete if you have the reputation to do so.)
elementary-set-theory game-theory lattice-orders
asked Dec 24 '18 at 23:59
Jim RatliffJim Ratliff
1011
$endgroup$
As much as I do appreciate the contributions on m.se, I need to be able to cite a primary source for definitions related to partitions, e.g., what a refinement/coarsening is, coarsest common refinement, etc.
There must exist a text that covers it, because this question, "refinement of partition clarification," quotes from one but references it only as "my book."
I run across these concepts in game theory, discussions of common knowledge, etc., but--as is typically the case when math is discussed in an allied field--the requisite concepts/theorems are exploited but without citation.
I'm not sure exactly what field covers this. I've heard set theory conjectured and then rebutted.
(I've seen "join" equated to coarsest common refinement, suggesting this might be covered by lattice theory, but when I browse tables of contents for lattice-theory books, they don't obviously cover these partition concepts.)
From game theory, I'm all too familiar with "folk knowledge" that is passed down from generation to generation without being systematically codified. I'm hoping that these concepts have escaped that category.
(If either of my tags is off-target, feel free to delete if you have the reputation to do so.)
elementary-set-theory game-theory lattice-orders
elementary-set-theory game-theory lattice-orders
asked Dec 24 '18 at 23:59
Jim RatliffJim Ratliff
1011
asked Dec 24 '18 at 23:59
Jim RatliffJim Ratliff
1011
asked Dec 24 '18 at 23:59
Jim RatliffJim Ratliff
1011
asked Dec 24 '18 at 23:59
Jim RatliffJim Ratliff
1011
asked Dec 24 '18 at 23:59
Jim RatliffJim Ratliff
1011
1011
1
$begingroup$
The proper field is combinatorics. The partitions form a lattice (whether you mean integer partitions or set partitions) but it's a very special one, not a central object of study in massive theory.
$endgroup$
– Matt Samuel
Dec 25 '18 at 11:25
add a comment |
1
$begingroup$
The proper field is combinatorics. The partitions form a lattice (whether you mean integer partitions or set partitions) but it's a very special one, not a central object of study in massive theory.
$endgroup$
– Matt Samuel
Dec 25 '18 at 11:25
1
1
$begingroup$
The proper field is combinatorics. The partitions form a lattice (whether you mean integer partitions or set partitions) but it's a very special one, not a central object of study in massive theory.
$endgroup$
– Matt Samuel
Dec 25 '18 at 11:25
$begingroup$
The proper field is combinatorics. The partitions form a lattice (whether you mean integer partitions or set partitions) but it's a very special one, not a central object of study in massive theory.
$endgroup$
– Matt Samuel
Dec 25 '18 at 11:25
add a comment |
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$begingroup$
The proper field is combinatorics. The partitions form a lattice (whether you mean integer partitions or set partitions) but it's a very special one, not a central object of study in massive theory.
$endgroup$
– Matt Samuel
Dec 25 '18 at 11:25