# stroke sequence

Wed Dec 17 09:45:17 CET 2003

```    I will post the following comment to the  reference line of A002620.

%S A002620 0, 1, 2, 4, 6, 9, 12, 16, 20, 25, 30, 36, 42, ....

A(n) gives possible maximal numbers of strokes on  K_n.
Where all edges on K_n have directions.
A "stroke" is defined as follows :
A local maximal di-path on di- graph.
off set = 1

examples :
n=3 , two strokes are able to exist, "x -> y -> z" and " x -> z" , so
A(3)=2 .
n=4, maximal four strokes exist, "u -> x -> z" and "u -> y" and "u -> z"
and "x -> y -> z" , so A(4)=4 .

And one  more sequence :
%S A000001 0, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, ....
B(n) gives minimal numbers of strokes on  K_n.
If B(n)=1 then K_n has an Euler path.

[an introduction to stroke theory]

I suppose that probably graph theorists call a  stroke "a local maximal
di-path".
It is not so long, so it might not be necessary to have a name for it.
But for us, "stroke" is a natural idea.
A Kanji is recognized as a set of ordinal strokes.
ex.1
a graph of Kanji "Ta" which means a field and is the same as 2*2 grid.
._._._._.
|_._|_._|
|_._|_._|
names of vertices
v_00, v_01, v_02
v_10, v_11, v_12
v_20, v_21, v_22

If we use the idea "stroke", it is possible to say as follows.
A Kanji "Ta" is an ordinal  set of strokes such that

(v_00->v_10->v_20,
v_00->v_01->v_02->v_12->v_22,
v_10->v_11->v_12,
v_01->v_11->v_21,
v_20->v_21->v_22).

where x->y->z means di-path from x to z.

ex.2
a graph of zero or "kuchi" which means a mouth and is the same as a
square.
._._.
|_._|
names of vertices
v_00, v_01
v_10, v_11

It is possible to distinguish "zero" and "kuchi".

"zero" is represented as
(v_00->v_10->v_11->v_01->v_00)

"kuchi" is represented as
(v_00->v_10, v_00->v_01->v_11, v_10->v_11)

jon awbrey wrote :

>i seem to remember frank harary writing something on
>a similar sort of "calli-graphic" theme a few years
>back -- i think it was in the journal 'leonardo'?

Thanks for the information.
I want to read his study.

Edwin Clark wrote :

>I don't know if there is a standard name. The only thing I could find
>searching MathSciNet is the following paper (which I don't have-so I don't
>know what their definition is.)

----------

I assume that the Chinese and Japanese use the same stroke sequences in
writing characters:

MR0699663 (84e:68115)
Zhang, Xin Zhong; Xia, Ying; Sun, Cheng Jian
An investigation of the recognition of handprinted Chinese characters by
stroke extraction. (Chinese. English summary)
Chinese J. Comput. 5 (1982), no. 6, 455--462.
68G10
----------------------------------------------------------------------------
----
Authors' summary: "In this paper a method of recognizing handprinted
Chinese characters by stroke extraction and composition is proposed, and
preliminary experimental results are presented. About one hundred and
fifty handprinted Chinese characters are simulated. We show that the
method of stroke extraction and composition is satisfactory for
recognition of regularly handprinted characters. It is expected that a
recognition system for handprinted and multifont printed Chinese
characters will be implemented by further improvements, including the
application of post-processing."
-----------------------------------------------------------------------

The study seems to be about an automatic recognition of handprinted
Kanji.
Their method "stroke extraction and composition" may be the same as my
representation described in this mail.     .

>PS.
>Mukashi, mukashi, watakushi wa Nihongo o benkyo shimashita.
>Shikashi, hotondo minna wasuremashita :-)

I translate it in English. The last one is a Japanese smiley.
>I studied Japanese, but it was a long time ago, so I have forgotten
almost all.  ^o^

I feel sorry. Study again !!
I am sure that Japanese culture is a wonderland.

Yasutoshi

```