# Bell number

Henry Gould gould at math.wvu.edu
Fri Apr 25 18:01:28 CEST 2003

```Ohaio Gozaimas!

Yes, this is because the old Japanese in the 1700's used incense diagrams
based on arrangements of different or same sticks of incense to label
the 52 inner chapters of the Genji Monogatari (Tale of Genji) that was
originally written by Lady Shikibo Murasaki around 1002 A.D. Each
chapter of Lady Murasaki's novel about Prince Genji and his love had
a designation, e.g. like "young violet" etc. I do not believe we know
yet why a given incense (partition) diagram was associated with a
chapter of the Genji Monogatari.

I have a booklet about Bell and Catalan Numbers, where the Murasaki
Diagrams are shown; however at the time I put that together I did not
add in the Japanese names for each diagram. I will do that in my
revised booklet, which lists over 450 references from antiquity up to
about 1980 for Catalan and maybe 250 for Bell numbers.

A writer in Japan sent me copies of some pages from an illustrated
Tale of Genji dating to 1700's. I would dearly like to procure a
complete copy.

Tale of Genji was translated into English many years ago by
Arthur Waley, but lacks the lovely incense ceremony stick diagrams.

Sayonara,

Henry Gould

"y.kohmoto" wrote:

>     Hello, seqfans.
>     I think Japanese is the most mathematical language.
>     Because it has all names of partitions of an 5-element set.
>
>     "Genjikoh no zu"
>     http://plaza27.mbn.or.jp/~921/kumiko/genjiko/genjikou.html
>     See this site. Before it please download Japanese character set.
>
>     You can see all figures and kanjis and names of 52 cases which is 5-th
> term of Bell number.
>
>     For example, No.5 represents {1,2}{3,4}{5}.
>     You will understand easily the law of figure. At a cross point, it is
> not jointed.
>     Next line, you see the kanji which means "young violet".
>     Last line, the name "waka murasaki"
>
>     Yasutoshi

```