The intuitive correspondence between the multiplication schemes (or triangularizations) and -1s 1s sequences.

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I am reading Richard A. Brualdi 's book Introductory Combinatorics (5th Edition).

In p.273, the author introduced the correspondence between the multiplication schemes for the n numbers a1, a2, ... and triangularizations of convex polygonal regions of n + 1 sides.

It is very intuitive.

However, how does the multiplication schemes (or triangularizations) corresponds to the -1s 1s sequences in p.266.

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Is there any intuitive way to turn the -1s 1s sequences problem to the multiplication schemes (or triangularizations)?

Very thanks.