論文の公開元へSome explicit formulae for the distributions of words (Probability Symposium)
概要
Thed
i
s
t
r
i
b
u
t
i
o
n
so
ft
h
enumbero
ft
h
ea
p
p
e
a
r
a
n
c
e
so
fwords(
d
i
s
t
r
i
b
u
t
i
o
n
so
fwordsf
o
rs
h
o
r
t
)p
l
a
y
i
m
p
o
r
t
a
n
tr
o
l
ei
ns
t
a
t
i
s
t
i
c
s
,DNAa
n
a
l
y
s
i
s
,i
n
f
o
r
m
a
t
i
o
nt
h
e
o
r
y
,s
e
eB
a
l
a
k
r
i
s
h
n
a
ne
t
.
a
l[
1
]
,J
a
c
q
u
e
t
e
t
.
a
l[
1
3
]
,L
o
t
h
i
r
ee
t
.
a
l[
1
5
]
,Robine
t
.
a
l[
2
1
]
,Walde
t
.
a
l[
2
5
]
,Waterman[
2
6
]
,andZ
e
h
a
v
ie
t
.
a
l[
2
7
]
.
G
e
n
e
r
a
t
i
n
gf
u
n
c
t
i
o
n
so
ft
h
ed
i
s
t
r
i
b
u
t
i
o
n
so
fwordsa
r
eg
i
v
e
na
sr
a
t
i
o
n
a
lf
u
n
c
t
i
o
n
s
,s
e
eB
a
s
s
i
n
o
e
t
.
a
l[
2
]
,B
e
r
t
h
ee
t
.
a
l[
3
]
,Blome
t
.
a
l[
4
]
,Chrysaphinoue
t
.
a
l[
5
]
,F
e
l
l
e
r[
6
]
,F
l
a
j
o
l
e
te
t
.
a
l[
7
]
,Goulden
e
t
.
a
l[
1
0
]
,Guibase
t
.
a
l[
1
1
]
,and即 g
n
i
e
re
t
.
a
l[
2
0
]
.Fromg
e
n
e
r
a
t
i
n
gf
u
n
c
t
i
o
n
s
,weh
a
v
ea
p
p
r
o
x
i
m
a
t
i
o
n
sandr
e
c
u
r
r
e
n
c
ef
o
r
m
u
l
a
ef
o
rt
h
ed
i
s
t
r
i
b
u
t
i
o
n
so
fw
o
r
d
s
. Howevere
x
c
e
p
tf
o
rs
i
m
p
l
ec
a
s
e
s
,we
n
e
i
t
h
e
rexpandr
a
t
i
o
n
a
lf
u
n
c
t
i
o
n
si
n
t
opowers
e
r
i
e
sn
o
ro
b
t
a
i
nt
h
e
i
rc
o
e
f
f
i
c
i
e
n
t
sbyd
i
f
f
e
r
e
n
t
i
a
t
i
o
n
,
s
e
eChapter1
1S
e
c
t
i
o
n4p
p
.2
7
5F
e
l
l
e
r[
6
]
.I
no
t
h
e
rw
o
r
d
s
,wec
a
n
n
o
to
b
t
a
i
ne
x
p
l
i
c
i
tf
o
r
m
u
l
a
ef
o
r
t
h
ed
i
s
t
r
i
b
u
t
i
o
n
so
fwordsfromr
a
t
i
o
n
a
lg
e
n
e
r
a
t
i
n
gf
u
n
c
t
i
o
n
si
ng
e
n
e
r
a
l
.
.t
h
ej
o
i
n
td
i
s
t
r
i
b
u
t
i
o
n
so
fn
o
n
o
v
e
r
l
a
p
p
i
n
gwords
I
nt
h
i
sa
r
t
i
c
l
eweshowe
x
p
l
i
c
i
tf
o
r
m
u
l
a
ef
o
r1
f
o
ri
n
d
e
p
e
n
d
e
n
tandi
d
e
n
t
i
c
a
l
l
yd
i
s
t
r
i
b
u
t
e
d(
i
.
i
.
d
.
)f
i
n
i
t
ea
l
p
h
a
b
e
trandomv
a
r
i
a
b
l
e
sand2
.t
h
e
d
i
s
t
r
i
b
u
t
i
o
n
so
fr
u
n
sf
o
ri
.
i
.
d
.b
i
n
a
r
yrandomv
a
r
i
a
b
l
e
s
. ...
この論文で使われている画像
