How can I simply write the expression :$y_1 y_2 x_3 x_4x_5+ y_1y_3x_2x_4 x_5+\cdots$

Question

How can I simply write the expression: $$y_1 y_2 x_3 x_4x_5+ y_1y_3x_2x_4 x_5+\cdots=$$ using $\sum $ and $\prod$? Any help will be appreciated. Thanks.

score 5 · Accepted Answer · answered Feb 24 '19 at 18:42

5

Whether this really counts as "simple" is perhaps open to debate: $$ \sum_{S\subset\{1,2,3,4,5\}\atop |S|=2}\;\,\prod_{i\in S}y_i\prod_{i\in\{1,2,3,4,5\}\setminus S}x_i$$

answered Feb 24 '19 at 18:42

Hagen von Eitzen

374,180

Thank you very much Hagen. I agree. It doesn't look any simpler but that's exactly what I was looking for. Great sense of humor by the way. Thanks once again. – Numberphile Feb 24 '19 at 19:02

How can I simply write the expression :$y_1 y_2 x_3 x_4x_5+ y_1y_3x_2x_4 x_5+\cdots$

1 Answers1