[seqfan] Re: A263484

[Fred Lunnon]

   I confirm AW's suggested amendments.

  A dumb Maple program finds the table for  n <= 10  in ~ 2 mins
as follows ---

[1]
[1, 1]
[1, 2, 3]
[1, 3, 7, 13]
[1, 4, 12, 32, 71]
[1, 5, 18, 58, 177, 461]
[1, 6, 25, 92, 327, 1142, 3447]
[1, 7, 33, 135, 531, 2109, 8411, 29093]
[1, 8, 42, 188, 800, 3440, 15366, 69692, 273343]
[1, 9, 52, 252, 1146, 5226, 24892, 125316, 642581, 2829325]

The complete program utilises my own bagperm generator,
so currently runs to 50 lines.

WFL



On 6/12/19, Allan Wechsler <acwacw at gmail.com> wrote:
> I am pretty sure the sequence name is garbled, though the Richard Stanley
> paper makes it pretty clear what's going on. So in the hopes that a simple
> English description will answer your question, here is one:
>
> Suppose we are permuting the numbers from 1 through 5. For example,
> consider the permutation (1,2,3,4,5) -> (3,1,2,5,4). Notice that there is
> exactly one point where we can cut this permutation into two consecutive
> pieces in such a way that no item is permuted from one piece to the other,
> namely (3,1,2 | 5,4). This "cut" has the property that all the indices to
> its left are less than all the indices to its right. There are no other
> such cut-points: (3,1 | 2,5,4) doesn't work, for example, because 3 > 2.
>
> Stanley defines the "connectivity set" as the set of positions at which you
> can make such a cut. In this case, the connectivity set is {3}.
>
> Is A263484, T(n,k) counts the number of permutations of n elements with k
> cut points.
>
> It looks to me like the name should have been "... the number of
> permutations of n elements with n-k elements in its connectivity set.", not
> "... with n!-k permutations ..."
>
>
>
>
>
> On Wed, Jun 12, 2019 at 1:23 PM jnthn stdhr <jstdhr at gmail.com> wrote:
>
>> Hi all.
>>
>>   Is there someone here with knowledge of connectivity sets of
>> permutations
>> who wouldn't mind improving A263484 by adding a program, extending the
>> sequence a bit more, and add an example, if it seems reasonable to do so?
>>
>>   The reason I ask is because I have a program that is apparently
>> producing
>> A236484, but don't understand why, and so don't know if I should add an
>> "Also,..." comment or not.
>>
>>   I have a short stackexchange post regarding this program here:
>>
>> https://math.stackexchange.com
>> /questions/3257689/why-does-this-appear-to-produce-oeis-sequence-a263484
>>
>> Thanks.
>>
>> --
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>
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