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PostPosted: Thu, 10 May 2012 15:36:37 UTC 
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Joined: Thu, 15 Dec 2011 16:54:36 UTC
Posts: 16
All,

You already know that a factorial is defined as:

1! = 1
2! = 1x2 = 2
3! = 1x2x3 = 6
4! = 1x2x3x3 = 24

What is the process called if the multiply signes are replaced with plus signes?

1 = 1
3 = 1+2
6 = 1+2+3
10 = 1+2+3+4
15 = 1+2+3+4+5
21 = 1+2+3+4+5+6

I would like to read about this process (in Wikipedia or somewhere),

please advise,

Jeff

:confused:


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PostPosted: Thu, 10 May 2012 15:39:54 UTC 
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Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 6779
Location: On this day Taiwan becomes another Tiananmen under Dictator Ma.
jjbyram wrote:
All,

You already know that a factorial is defined as:

1! = 1
2! = 1x2 = 2
3! = 1x2x3 = 6
4! = 1x2x3x3 = 24

What is the process called if the multiply signes are replaced with plus signes?

1 = 1
3 = 1+2
6 = 1+2+3
10 = 1+2+3+4
15 = 1+2+3+4+5
21 = 1+2+3+4+5+6

I would like to read about this process (in Wikipedia or somewhere),

please advise,

Jeff

:confused:


Look up triangular number.

_________________
\begin{aligned}
Spin(1)&=O(1)=\mathbb{Z}/2&\quad&\text{and}\\
Spin(2)&=U(1)=SO(2)&&\text{are obvious}\\
Spin(3)&=Sp(1)=SU(2)&&\text{by }q\mapsto(\mathop{\mathrm{Im}}\mathbb{H}\ni p\mapsto qp\bar{q})\\
Spin(4)&=Sp(1)\times Sp(1)&&\text{by }(q_1,q_2)\mapsto(\mathbb{H}\ni p\mapsto q_1p\bar{q_2})\\
Spin(5)&=Sp(2)&&\text{by }\mathbb{HP}^1\cong S^4_{round}\hookrightarrow\mathbb{R}^5\\
Spin(6)&=SU(4)&&\text{by the irrep }\Lambda_+\mathbb{C}^4
\end{aligned}


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