#### Alladi Ramakrishnan Hall

#### Proofs without words: the example of the Ramanujan continued fraction

#### Xavier Viennot

##### CNRS, France

*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.html

Done