[seqfan] Re: Number of knots with trivializing number k among all knots with n crossings
jvospost3 at gmail.com
Mon Aug 17 21:02:41 CEST 2009
Yes, I think so, Franklin T. Adams-Watters.
The paper seems to set some upper and lower bounds, which I am not
100% sure about.
Would you be willing to co-submit this with me? I'm having a severe
LAN problem at my home office, even after rebooting multiple PCs,
cable modem, router? Hence I also apologize for shouting fire in a
crowded seqfans theatre about wondering if OEIS was down. After
working with software/hardware systems since 1966, you'd think I'd run
end-to-end checks more often...
On the plus side, it gets me away from Facebook.
Jonathan Vos Post
On Mon, Aug 17, 2009 at 11:53 AM, <franktaw at netscape.net> wrote:
> Yes, this is definitely a good sequence for the OEIS.
> Yes, as I understand it, odd numbered columns should be eliminated. So
> the definition becomes something like "Table T(n,k) is the number of
> knots with n crossings and trivializing number 2k". This will then be
> a tabf sequence:
> Yes, this is the way to present it.
> Do we generally have 2k <= n - 3, so the row lengths are
> Franklin T. Adams-Watters
> -----Original Message-----
> From: Jonathan Post <jvospost3 at gmail.com>
> Number of knots with trivializing number k among all knots with n
> derived from Table 1, p.24, of
> Allison Henrich, Noel MacNaughton, Sneha Narayan, Oliver Pechenik,
> Jennifer Townsend,
> Classical and Virtual Pseudodiagram Theory and New Bounds on
> Unknotting Numbers and Genus
> n / k=1.|.k=2.|.k=3.|.k=4.|.k=5.|.k=6.|.
> n=3.|.0. |.1.|
> n=4.|.0. |.1.|
> The n=9 row of the table seems currently uncertain for some values of k.
> Is this good for OEIS? Should one eliminate the non-even k columns,
> per theorem in the paper? Is there a better presentation?
> Thank you,
> Jonathan Vos Post
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