24 
ON SEMIN VARIANTS. 
[801 
We may consider the question to determine the number of asyzygetic seminvariants 
of a given degree and weight. For instance, taking the weights up to 12, so that 
the series of letters extends as far as m, then for the degrees 1, 2, 3 we have as 
follows: 
w= 
0 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
Deg. 1 
a 
h 
c 
d 
e 
/ 
9 
A 
i 
j 
k 
* 
m 
Nos. 
1 
1 
1 
1 
1 
1 
1 
1 
1 
1 
1 
1 
1 
Diff. 
0 
o 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
Deg. 2 
№ 2 
ab 
ac 
ad 
ae 
af 
acj 
all 
ai 
aj 
ak 
al 
am 
b 2 
be 
bd 
be 
¥ 
¥ 
bh 
bi 
bj 
bk 
bl 
c 2 
cd 
ce 
¥ 
eg 
eh 
ci 
C J 
ck 
d 2 
de 
df 
dg 
dh 
di 
dj 
e 2 
¥ 
e 9 
eli 
ei 
r 
/9 
fh 
9 2 
Nos. 
1 
1 
2 
2 
3 
3 
4 
4 
5 
5 
6 
6 
7 
Diff. 
1 
0 
1 
0 
1 
0 
1 
0 
1 
0 
1 
0 
1 
Deg. 3 
a 3 
adb 
adc 
odd 
ode 
af 
a-g 
adh 
adi 
adj 
cdk 
odl 
adm 
ab 2 
abc 
abd 
abe 
abf 
abg 
abh 
abi 
abj 
abk 
abl 
ac 2 
acd 
ace 
acf 
aeg 
acli 
aci 
acj 
ack 
ad 2 
ade 
adf 
adg 
adli 
adi 
adj 
ad 
aef 
aeg 
aeh 
aei 
af 2 
<¥g 
afli 
ag 2 
b 3 
b 2 c 
b 2 d 
b 2 e 
bf 
b 2 g 
b 2 h 
b 2 i 
b 2 j 
b 2 k 
be 2 
bed 
bee 
bef 
beg 
bcli 
bci 
bej 
bd 2 
bde 
bdf 
bdg 
bdli 
bdi 
be 2 
bef 
beg 
beli 
bf 2 
¥9 
c 3 
c 2 d 
c 2 e 
of 
c 2 g 
dli 
<di 
cd 2 
ede 
cdf 
edg 
cdh 
ce 2 
cef 
ceg 
<¥ 2 
d 3 
d 2 e 
df 
d 2 g 
de 2 
def 
e 3 
Nos. 
1 
1 
2 
3 
4 
5 
7 
8 
10 
12 
14 
16 
19 
Diff. 
1 
0 
1 
1 
1 
2 
1 
i 
2 
2 
2 
2 
2 
3