[seqfan] Re: Partition into Stroke

[Allan Wechsler]

Yasutoshi, I urge caution.

The definitions at A131519 seem a little confusing and vague to me. For
example, I am guessing that you do *not* consider v1v2 + v3v2 to be a path,
even though it satisfies all the constraints that are stated. Other
constraints, not stated in A131519, are needed to make "path" correspond to
the usual definition of path in graph theory.

Because the definitions might be confusing, I suspect that Max Alexeyev,
who is a smart guy, interpreted them to mean something other than what you
intended. That means that the data listed in A131519 is counting *something*,
but perhaps not the same thing you *wanted* to count.

If that's the case, then what needs to happen is: (1) A131519 should be
clarified so that it clearly explains what Max was counting. (2) Introduce
a new sequence with your new data, clearly explaining what *it* is counting
(and explaining the difference from A131519). (3) Somebody will then step
up and provide more data, hopefully.

But A131519 is old enough now that there could easily be papers referring
to it in the mathematical literature, or on websites. So it is probably not
a good idea to alter the data at this late date.

I think it would help *me *if you could explicitly enumerate the 6 "stroke
partitions" of G2. I cannot find six of *anything* in G2. G2 only has two
edges, right?

Allan

On Fri, Jan 21, 2022 at 2:12 AM <zbi74583_boat at yahoo.co.jp> wrote:

> Hi  Seqfans    I abstracted the idea of "Stroke" which is used in writing
> Kanji.    For instance, when "木" is written, which means tree, these four
> strokes are used. See " How to write a" 's page
>     https://kakijun.jp/page/0461200.html
>     My definition of " Partition into stroke " which is an abstraction of
> Kanji 's stroke is the following
>     Given an undirected graph G=(V,E), its partition into strokes is a
> collection of directed edge-disjoint paths (viewed as sets of directed
> edges) on V such that (i) union of any two paths is not a path; (ii) union
> of corresponding undirected paths is E.
>
>     The other description of the definition is the following
>     A "stroke" is defined as follows. If the following conditions are
> satisfied then the partition to directed paths on a directed graph is
> called "a partition to strokes on a directed graph". And all directed paths
> in the partition are called "strokes". C.1. Two different directed paths in
> a partition do not have the same edges. C.2. A union of two different paths
> in a partition does not become a directed path. In other word, a "stroke"
> is a locally maximal path on a directed graph.
>     Recently  I recomputed the terms of A131519 and I have found it is
> fault
>     The correct one is    1, 6, 58, 490, ....    So  I am going to rewrite
> it  but I must confirm   it    Could anyone confirm   it and compute more
> terms ?    If the definition is difficult then feel free to ask anything
> about it
>
>
>     Yasutoshi
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>