[seqfan] Re: Number of knots with trivializing number k among all knots with n crossings
franktaw at netscape.net
franktaw at netscape.net
Mon Aug 17 20:53:48 CEST 2009
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:
1,1,0,1,1,2,1,5,6,1,11,9,...
Yes, this is the way to present it.
Do we generally have 2k <= n - 3, so the row lengths are
1,1,2,2,3,3,4,4,5,5,6,6,...?
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
crossings.
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
http://arxiv.org/PS_cache/arxiv/pdf/0908/0908.1981v1.pdf
n / k=1.|.k=2.|.k=3.|.k=4.|.k=5.|.k=6.|.
n=3.|.0. |.1.|
n=4.|.0. |.1.|
n=5.|.0.|.0.|.0.|..1.|
n=6.|.0.|.1.|.0.|..2.|
n=7.|.0.|.1.|.0.|..5.|.0.|.6.|
n=8.|.0.|.1.|.0.|.11.|.0.|.9.|
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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