[seqfan] Re: A263484

[Allan Wechsler]

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.
>
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