Proofs without words: the example of the Ramanujan continued fraction

Visual proofs of identities were common at the Greek time, such as the Pythagoras theorem. In the same spirit, with the renaissance of combinatorics, visual proofs of much deeper identities become possible. Some identities can be interpreted at the combinatorial level, and the identity is a consequence of the construction a weight preserving bijection between the objects interpreting both sides of the identity. In this lecture, I will give an example involving the famous and classical Ramanujan continued fraction. The construction is based on the concept of "heaps of pieces", which gives a spatial interpretation of the commutation monoids introduced by Cartier and Foata in 1969. For more informations? go to website of the combinatorial course "The Art of Bijective Combinatroics"? I am giving at IMSc (2016-2019) www.imsc.res.in/~viennot/abjc-course.htm