Talk:Permanent (mathematics)

message: Do permanents have anything to do with Bose statistics? I mean
is there something analogous to the Slater determinant using permanents?
: yes and yes. Permanents of one-particle wave functions span the Fock space (i.e., the space in which n-particle wave functions live) for bosonic particles. This is completely analogous to the Fermionic case where Slater determinants take the identical role.
: Note that unlike determinants, permanents do not vanish if multiple linear dependent vectors are inserted (if viewed as multi-linearform). Thus you can occupy orbitals an arbitrary number of times (i.e., put the same orbital multiple times into a permanent) to obtain non-vanishing n-body states. 129.69.55.52 (talk) 22:47, 27 March 2009 (UTC)
thread_title: Untitled

message: I'm unfamiliar with the concept of groups, and the more with symmetry-groups.
Would it be possible for me to compute the "permanent" anyway?
Say, I'm already familiar with the implementation of an algorithm
to compute the determinant, with a recursive method using
pivot elements; and stepping from the size 2x2-definition
to a 3x3-definition and higher recursively.
Also I know that there are shortcuts for the 3x3-matrix (but say this would be a special cases only applicable for computing determinants).
Then how could I compute the permanent of a 3x3 after I have the (simple) definition of a permanent of a 2x2 matrix?
With a 3x3-determinant of
 a0 b0 c0
 a1 b1 c1
 a2 b2 c2 
I can compute the determinant via the subdeterminants like
  a0 * det(b1,c2,c1,b2) - b0*det(c1,a2,c2,a1) + c0*det(a1,b2,b1,a2)
(don't know exactly about the signs at the moment)
Is there any way to compute the permanent similar without refering to the "symmetric group"-concept? (if I started learning about groups and symmetric groups I assume I would have a lot of errors in the beginning and would not be able to determine the permanent correctly).
Thanks -
--Gotti 10:31, 13 January 2007 (UTC)
thread_title:  how to compute 

message: "The permanent is also more difficult to compute than the determinant."
Is this known to be true or is it based on an unproven assumption?  —Preceding unsigned comment added by Deepmath (talk • contribs) 01:52, 12 March 2008 (UTC)
replies: text: I think the current article explains this now; its a result from complexity theory for the #P subset of NP. 99.153.64.179 (talk) 23:20, 5 July 2013 (UTC)
thread_title:  Complexity 

message: This edit added a number of applications of the permanent to this section, nicely explained and with references. In principle, this addition is welcome, but I‘d never heard of them. An (admittedly rushed) glance at Google Scholar brings up little evidence that these things have had a considerable impact (I may be wrong.) Anonymous IP, could you provide a secondary source that motivates their inclusion? (It sounds really interesting, and I’d be happy to keep it around.) Also, could you please state if you have any conflict of interest in including these results (see WP:COI for Wikipedia’s policies)? Let me stress that the contributions of experts are very welcome, but it helps other editors to be open about such conflicts in order to ascertain what kind of weight is to be given to various contributions. Thore Husfeldt (talk) 19:09, 15 December 2009 (UTC)
replies: text: I’ve reverted the anonymous edit. I’m happy to put it back if somebody, such as  128.206.20.161, makes a case for the relevance of these additions. Thore Husfeldt (talk) 19:52, 16 December 2009 (UTC)

text: The added text appears here:  and its about the joint assignment matrix. The added text is rather long and perhaps should be used to start the JAM article instead. 99.153.64.179 (talk) 23:30, 5 July 2013 (UTC)
thread_title:  Applications added by 128.206.20.161 

message: I'm just curious.  Given that the permanent is related to the determinant and the immanant, is the correct spelling permanent or permanant?  70.247.173.254 (talk) 20:14, 22 July 2012 (UTC)
replies: text: Correct spelling is permanent. The terms permanent and determinant both appear in Cauchy in 1812 with their modern definitions, but each had appeared earlier in unrelated forms. Thus their spellings are not related. Bill Cherowitzo  (talk) 23:05, 22 July 2012 (UTC)
thread_title:  Spelling 

message: Substituted at 02:28, 5 May 2016 (UTC)
thread_title: Assessment comment

message: Having implemented in APL Ryser's algorithm for the Permanent, I tested that algorithm against the two formulae given in the section on "Permanents of (0,1) matrices".  In the case of the ménage problem, it appears that the statement of the number of solutions to that problem (Touchard's formula on the right hand side) is correct, but that \operatorname{perm}(J - I - I') actually produces ménage numbers, that is Touchard's formula without the leading 2×n!.  As the equation as it currently stand mixes these two concepts, I'm not sure how to reword it to make sense, and am hoping that you folks who are more familiar with the topic will suggest something. Sudleyplace (talk) 00:47, 9 March 2018 (UTC)
replies: text: Yes, you're absolutely right.  There is ambiguity about what people mean when they say "the ménage problem" (whether the original seating problem or the simplified permutation problem), and so I think that removing the extra factor 2×n! from the formula in the article leaves something that is not wrong and also understandable (as opposed to the current "wrong and understandable").  --JBL (talk) 14:34, 9 March 2018 (UTC)
thread_title: Use of Touchard's Formula

message: I see that Gyires published a proof of Van der Waerden's conjecture before two others who got a prize for theirs. Does anyone know why? It seems odd and a little unfair, and quite likely to be worth a mention here! I could only access Egorychev's proof, and saw nothing about Gyires in the references. PJTraill (talk) 21:02, 22 April 2022 (UTC)
replies: text: This is pure speculation, but I would guess that the obscure venue of Gyires’s publication played a role — quite possibly, nobody else relevant knew about it. JBL (talk) 17:11, 24 April 2022 (UTC)
thread_title:  Why did Gyires not get a prize for his proof of the Van der Waerden conjecture? 

message: https://doi.org/10.1016/j.laa.2015.10.034
I think this has relevance for the actual physics of photon bunching, https://arxiv.org/pdf/2203.01306.pdf
Worth pointing out a physics discovery resulting from a math proof 156.40.187.164 (talk) 16:17, 5 September 2023 (UTC)
thread_title:  The permanent-on-top conjecture is false