User blog:Nayuta Ito/Piling Up Notation(2)

In previous article, I made up to polynomial. My next goal is multidimensional.

Then, what should the next notation be? Just piling up.

$$PU(1(1)a)=PU(a,a,\cdots,a,a)\,(atimes)$$

Next, what is PU(1(1)a,b)? Just piling up again. Piling up starts from 2 entries unless there us nothing else.

$$PU(1(1)a,b)=PU(1(1)a-1,PU(1(1)a,b-1))$$

This means a,b piles up b (a-1)'s.

Other things is the same as one-ray, so:

Now, I will jump to polynominal. K means some one's. M is somehting and sometimes nothing.

$$PU(Ma,b,c,d,\cdots)=PU(a,PU(a,b-1,c,d,\cdots),c-1,d,\cdots)$$

$$PU(Ma,b,K,1,d,\cdots)=PU(a,b,K,PU(a,b-1,K,1,d,\cdots),d-1,\cdots)$$

$$PU(Ma,1,X)=a$$

$$PU(a(1)b)=PU(a-1(1)b,b,\cdots,b,b)\,(btimes)$$

$$PU(Ma,b)=PU(Ma-1,PU(Ma,b-1))$$ if M is not nothing

$$PU(a,b)=a^b$$ (if M is nothing)

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