fee es - math.columbia.edu
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mn inm FEE ESAigner How many words length 2
I letter 2kWA
iC Z
3 3
Binomial coefficients
L nchoosek numberof subsets
of shek of n things
6 142 ABcD_xxx xx xxxx xxx
1 Pascal's 8i Triangle lo t
3 I C ohtI 46 4 1 13 G CEI 3I 5 10 10 S 1
YT F tiny divideand conquer
E Z E
421 6yess
1 7 12131402234 thy 2 2324340pick 2 use 1
YT E tina HH CH
RE lRzMxt moRxtESfCx
sgcm egcntd g.cn
gCnI KAgin n H Ii
Eek S2 znttz 2no
nnx 87,677,121,13
bx x3x3NNN
FEELIt 21,31 4 10
t
Er im for any power M 1
gcn It 2T the
Sgcn gchti gcn htt 7 no
and_n9nE Tiantai
81 1
Cilento
2 MID gin 2 67 tf2 ncn 2 _n n
NAHI
L overbunting2
n all permutationsof l h Coranynthings
na n D 3.2 I
21 3g 123
n 1 132
2 213
231B 2 3123.2 1 6 321
4 I nE E I a _2z6
tokeep discard
ignore order
12 13 14
Gt3 Ltg Gt3 Ltg Gt3Lte
12 43 21 43 1342 31 42 14 32 0413223 24 34
8241405644 Gt3 tog GYUto
2341 3241 24 31 4231 3421 04321
41.121.2I
1 ftp.kyZ38
K keep n k discard
87.6 5.4 3.213.2l S U 3.2 I
4 287.8317
56
ba s agummt
howmany monomials of degd inn variablesterms
n 3 X 4,2 0 0 X 4920 1
0 1 X Y Z
D 2 1544923 4 2,42
0 3 19,4323 24 24,43 22,423422 XYZ
cP'Fant'asugie ETI y f z
I 2 I 111 a It
i's I YIi.E.i.iX.lloy2ElonIy21
1 I421 6 22 9 Hoo
deg3 in Nycz 2 dividers Xl4123 balls ooo
ql.dz EY E 542 10
Xyz alot