Double Decks choose m cards from 2 decks of n cards 1+e+=∑(e+2* 会0-）得 p<k :
k k x Double Decks 2 deck of s n cards choose m cards from (1 + x + x2) n = k n k (x + x2) k = k n k xk = k k n k k xk+ = m n m m xm ( )
Multisets multisets on S={1,2,...,n (1+x1+c+…)(1+x2+c2+…)…(1+xm+x2+…) =∑Ⅱa) m:S→Nxi∈S +-+=(》 ll geometric m∈Nn (1-x）n=∑-m(-n-1）(-n-k+1)(-1)xk k! k≥0 Taylor
Multisets multisets on (1 + x1 + x2 1 + ···)(1 + x2 + x2 2 + ···)···(1 + xn + x2 n + ···) S = {x1, x2,...,xn} = m:SN ⇥ xi⇥S x m(xi) i (1 + x + x2 + ···) n = ⇤ k0 n k ⇥⇥ xk = m⇥Nn xm1+···+mn (1 x) n = k0 (n)(n 1)···(n k + 1)(1)k k! xk = geometric Taylor
Multisets multisets on S={1,22,...,n} (1+1++…)(1+x2+c2+…）…(1+xn+x2+…) =∑Ⅱa) m:S→Nxi∈S +++=∑*m=() m∈Nn k>0 川 1-”=(+会-)
Multisets multisets on (1 + x1 + x2 1 + ···)(1 + x2 + x2 2 + ···)···(1 + xn + x2 n + ···) S = {x1, x2,...,xn} = m:SN ⇥ xi⇥S x m(xi) i (1 + x + x2 + ···) n = ⇤ k0 n k ⇥⇥ xk = m⇥Nn xm1+···+mn (1 x) n = k0 xk n + k 1 k = n k = n + k 1 k
Ordinary Generating Function (OGF) {an} 00,a1,a2,··· generating function: ●X● G(=anx”=a0+a1x+a22+… m=0 [x"]G(x)=an
Ordinary Generating Function (OGF) G(x) = n=0 anxn = a0 + a1x + a2x2 + ··· {a a0, a1, a2,... n} generating function: [xn]G(x) = an
Fibonacci number Fn-1+Fn-2ifn≥2， if n =1 fm=0
Fibonacci number Fn = ⌅⇤ ⌅⇥ Fn1 + Fn2 if n 2, 1 if n = 1 0 if n = 0