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