The Art of Bijective Combinatorics    Part I 

An introduction to enumerative, algebraic and bijective combinatorics

 

The Institute of Mathematical Sciences, Chennai, India  (January-March 2016)

Ch 0  Introduction to the course

 

    5 January 2016

 

                               slides_Ch0     (pdf   25 Mo)             video Ch 0       (1h 10mn)

 

 

enumerative combinatorics 3    0:50    

an example with Young tableaux 5    2:08 

Hook-length formula 10    6:12  

another example with binary trees, the use of ordinary generating functions  19      9:34

an example with alternating permutations, the use of exponential generating functions 35     17:05

bijective combinatorics, example: planar maps 42    29:35

bijective proof of an identity, example RSK  48     35:10

algebraic combinatorics 55      39:50

the bijective paradigm 62    43:55

example: Mehler identity for Hermite polynomials 64    45:20

identities, bijections, « bijective tools »  84     55:41

example: hook-length formula and number of tilings of the  Aztec diagram under the same roof 89    59:33

another example: heaps of pieces 95    1:04:11

map of the course 97     1:05:31  

other courses    98     1:08:50

the end 98      1:09:52  

 

The  playlist from matsciencechannel of the 17 videos of this course is here