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This edit request by an editor with a conflict of interest has now been answered. |
After being informed by MrOllie about a potential conflict of interest, I am now formally requesting to make the following additions to the page. The Combinatorial Object Server is a collection of open source software tools I frequently use to create this kind of illustrations, and to which I am a frequent contributor.
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A: Add the following paragraph to the Subsection "Generation with minimal changes": The following figure shows the output of all three aforementioned algorithms for generating all permutations of length , and of six additional algorithms described in the literature. 1: Lexicographic ordering; 2: Steinhaus-Johnson-Trotter algorithm; 3: Heap's algorithm; 4: Ehrlich's star-transposition algorithm (see [2]): in each step, the first entry of the permutation is exchanged with a later entry; 5: Zaks' prefix reversal algorithm [3]: in each step, a prefix of the current permutation is reversed to obtain the next permutation; 6: Sawada-Williams' algorithm [4]: each permutation differs from the previous one either by a cyclic left-shift by one position, or an exchange of the first two entries; 7: Corbett's algorithm [5]: each permutation differs from the previous one by a cyclic left-shift of some prefix by one position; 8: Single-track ordering [6]: each column is a cyclic shift of the other columns; 9: Single-track Gray code [6]: each column is a cyclic shift of the other columns, plus any two consecutive permutations differ only in one or two transpositions. B: Add the following external link: References
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Torsten Mütze ( talk) 19:07, 29 May 2019 (UTC)
In permutations with repetitions it has to be stated at least Tuple#n-tuples_of_m-sets as the word tuples alone is only the plural of tuple (ordered set or list) so ordered sets or lists and permutations without repetitions refers to a scalar number
It has to be clarified Tuples at least as Tuple#n-tuples_of_m-sets as Tuples alone is only the plural of Tuple and Permutations without repetition is a scalar number. Orendona ( talk) 20:42, 1 November 2020 (UTC)
That is the use, they are not tuples, they are a special kind of tuples: All the possible tuples that can be made with repeated or not members of a second set. And they are not permutations. Some of the tuples are permutations of others. Orendona ( talk) 13:16, 3 November 2020 (UTC)
Adding real notations in notation subtopic will help people new to this and it makes article more easy to read. Anish59312 ( talk) 04:59, 13 July 2021 (UTC)
In the examples, slot numbers and values both use numbers, hiding the fact that the two are not the same. I propose that slots be identified by numbers, while values are letters. Comfr ( talk) 16:50, 16 August 2021 (UTC)
When the lede moves from the intuitive notion of permutation as a rearrangement to the technical definition as a bijection, I'm afraid it just gives the passive "permutation", instead of properly constructing the function f that would actively perform the rearrangement, i.e. by moving the element i to the place f(i).
Specifically, the informal "permutation" which is the arrangement (3, 1, 2) of the numbers {1, 2, 3} should correspond to the function accomplishing this arrangement by putting element i into place , which implies and . The permutation presently given is actually the inverse, .
The preceding statement "This is related to the rearrangement..." suffers from the same confusion, on top of mistakenly "rearranging" an arbitrary (unordered) set S. I suggest that this sentence should be removed while a similar, corrected, explanation is adapted to the specific example and inserted into the following sentence. –– St.nerol ( talk) 21:16, 16 September 2021 (UTC)
The Cycle Notation section explains that many different cycle notations are possible for the same permutation because the starting point for each cycle can be any element in the cycle and then it goes on to give examples; however, the first example given, (125)(34)=(34)(125), is of two equivalent cycles whose order is commuted but whose starting points are unchanged.
This is doubly confusing because the article clearly states that permutations do not in general commute but does not mention that an exception to this general rule is when the permutations are disjoint.
My suggestion is either to move the (125)(34)=(34)(125) example to its own separate paragraph which explains that disjoint permutations commute and hence give rise to multiple cycle notations for the same permutation or to reword the current paragraph in line with my edit at 19:07, 21 January 2022. Obtuse Wombat ( talk) 19:23, 23 January 2022 (UTC)
Here is the problem:
I hesitate to fix this problem myself, but my tentative plan is to delete the last sentence in Permutation#Permutations_without_repetitions, i.e., the one that begins,
Then I will go back to Partial permutation#Restricted partial permutations, and rewrite the sentence with the words "confusingly called".
Yours truly, Guy vandegrift ( talk) 03:38, 24 January 2022 (UTC)
Which term should be used to describe the type of a permutation in this article: "cycle type" or "cycle structure"? Both are common but Google gave 23,900 hits on my search for 'permutation "cycle type"' and 32,900 hits for 'permutation "cycle structure"', so on 6 August 2022 I edited the article to consistently use "cycle structure" (but mentioned that "cycle type" was also used). This edit was reverted, so I posted this talk page section to discuss the issue. Prior, to my earlier 30 July 2022 edit, this page confusingly used four terms to refer to the same thing ("cycle type" 3 times, "cycle structure" 1 time, "permutation type" 1 times, and "type" (by itself) 2 times). Based on the Google stats, I think it would be best to use "cycle structure" and mention "cycle type" as an alternative term. Even if we stick with the reversion to "cycle type", "cycle structure" should be mentioned as an alternative term. Obtuse Wombat ( talk) 19:06, 7 August 2022 (UTC)
People who have visual disabilities -- most notably color blindness -- can have problems with the Permutations example graphic. Instead of having all circles/balls, why not have different shapes? Colors could still be used for clarity, but there are some common pairs of colors to try to avoid, like red-green or green-blue. Keeping a high contrast for those who have issues with contrast is also important. To help contrast, maybe highlight each shape with a white or black outline, etc. Or, just use black & white for the different symbols.
Any graphic should have proper ALT text explaining what is visually in the image, of course. ALT text would not explain the mathematical significance; that's left for the image caption. Wikispherion ( talk) 16:52, 25 January 2023 (UTC)
Is this meant to indicate that σ is a bijective function? Klauscougar ( talk) 21:26, 29 October 2023 (UTC)
This
level-4 vital article is rated B-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
|
Daily pageviews of this article
A graph should have been displayed here but
graphs are temporarily disabled. Until they are enabled again, visit the interactive graph at
pageviews.wmcloud.org |
This page has archives. Sections older than 365 days may be automatically archived by Lowercase sigmabot III when more than 10 sections are present. |
This edit request by an editor with a conflict of interest has now been answered. |
After being informed by MrOllie about a potential conflict of interest, I am now formally requesting to make the following additions to the page. The Combinatorial Object Server is a collection of open source software tools I frequently use to create this kind of illustrations, and to which I am a frequent contributor.
Extended content
|
---|
A: Add the following paragraph to the Subsection "Generation with minimal changes": The following figure shows the output of all three aforementioned algorithms for generating all permutations of length , and of six additional algorithms described in the literature. 1: Lexicographic ordering; 2: Steinhaus-Johnson-Trotter algorithm; 3: Heap's algorithm; 4: Ehrlich's star-transposition algorithm (see [2]): in each step, the first entry of the permutation is exchanged with a later entry; 5: Zaks' prefix reversal algorithm [3]: in each step, a prefix of the current permutation is reversed to obtain the next permutation; 6: Sawada-Williams' algorithm [4]: each permutation differs from the previous one either by a cyclic left-shift by one position, or an exchange of the first two entries; 7: Corbett's algorithm [5]: each permutation differs from the previous one by a cyclic left-shift of some prefix by one position; 8: Single-track ordering [6]: each column is a cyclic shift of the other columns; 9: Single-track Gray code [6]: each column is a cyclic shift of the other columns, plus any two consecutive permutations differ only in one or two transpositions. B: Add the following external link: References
|
Torsten Mütze ( talk) 19:07, 29 May 2019 (UTC)
In permutations with repetitions it has to be stated at least Tuple#n-tuples_of_m-sets as the word tuples alone is only the plural of tuple (ordered set or list) so ordered sets or lists and permutations without repetitions refers to a scalar number
It has to be clarified Tuples at least as Tuple#n-tuples_of_m-sets as Tuples alone is only the plural of Tuple and Permutations without repetition is a scalar number. Orendona ( talk) 20:42, 1 November 2020 (UTC)
That is the use, they are not tuples, they are a special kind of tuples: All the possible tuples that can be made with repeated or not members of a second set. And they are not permutations. Some of the tuples are permutations of others. Orendona ( talk) 13:16, 3 November 2020 (UTC)
Adding real notations in notation subtopic will help people new to this and it makes article more easy to read. Anish59312 ( talk) 04:59, 13 July 2021 (UTC)
In the examples, slot numbers and values both use numbers, hiding the fact that the two are not the same. I propose that slots be identified by numbers, while values are letters. Comfr ( talk) 16:50, 16 August 2021 (UTC)
When the lede moves from the intuitive notion of permutation as a rearrangement to the technical definition as a bijection, I'm afraid it just gives the passive "permutation", instead of properly constructing the function f that would actively perform the rearrangement, i.e. by moving the element i to the place f(i).
Specifically, the informal "permutation" which is the arrangement (3, 1, 2) of the numbers {1, 2, 3} should correspond to the function accomplishing this arrangement by putting element i into place , which implies and . The permutation presently given is actually the inverse, .
The preceding statement "This is related to the rearrangement..." suffers from the same confusion, on top of mistakenly "rearranging" an arbitrary (unordered) set S. I suggest that this sentence should be removed while a similar, corrected, explanation is adapted to the specific example and inserted into the following sentence. –– St.nerol ( talk) 21:16, 16 September 2021 (UTC)
The Cycle Notation section explains that many different cycle notations are possible for the same permutation because the starting point for each cycle can be any element in the cycle and then it goes on to give examples; however, the first example given, (125)(34)=(34)(125), is of two equivalent cycles whose order is commuted but whose starting points are unchanged.
This is doubly confusing because the article clearly states that permutations do not in general commute but does not mention that an exception to this general rule is when the permutations are disjoint.
My suggestion is either to move the (125)(34)=(34)(125) example to its own separate paragraph which explains that disjoint permutations commute and hence give rise to multiple cycle notations for the same permutation or to reword the current paragraph in line with my edit at 19:07, 21 January 2022. Obtuse Wombat ( talk) 19:23, 23 January 2022 (UTC)
Here is the problem:
I hesitate to fix this problem myself, but my tentative plan is to delete the last sentence in Permutation#Permutations_without_repetitions, i.e., the one that begins,
Then I will go back to Partial permutation#Restricted partial permutations, and rewrite the sentence with the words "confusingly called".
Yours truly, Guy vandegrift ( talk) 03:38, 24 January 2022 (UTC)
Which term should be used to describe the type of a permutation in this article: "cycle type" or "cycle structure"? Both are common but Google gave 23,900 hits on my search for 'permutation "cycle type"' and 32,900 hits for 'permutation "cycle structure"', so on 6 August 2022 I edited the article to consistently use "cycle structure" (but mentioned that "cycle type" was also used). This edit was reverted, so I posted this talk page section to discuss the issue. Prior, to my earlier 30 July 2022 edit, this page confusingly used four terms to refer to the same thing ("cycle type" 3 times, "cycle structure" 1 time, "permutation type" 1 times, and "type" (by itself) 2 times). Based on the Google stats, I think it would be best to use "cycle structure" and mention "cycle type" as an alternative term. Even if we stick with the reversion to "cycle type", "cycle structure" should be mentioned as an alternative term. Obtuse Wombat ( talk) 19:06, 7 August 2022 (UTC)
People who have visual disabilities -- most notably color blindness -- can have problems with the Permutations example graphic. Instead of having all circles/balls, why not have different shapes? Colors could still be used for clarity, but there are some common pairs of colors to try to avoid, like red-green or green-blue. Keeping a high contrast for those who have issues with contrast is also important. To help contrast, maybe highlight each shape with a white or black outline, etc. Or, just use black & white for the different symbols.
Any graphic should have proper ALT text explaining what is visually in the image, of course. ALT text would not explain the mathematical significance; that's left for the image caption. Wikispherion ( talk) 16:52, 25 January 2023 (UTC)
Is this meant to indicate that σ is a bijective function? Klauscougar ( talk) 21:26, 29 October 2023 (UTC)