Dominique Foata : A Neoclassical Combinatorial Giant

Dominique Foata : A Neoclassical Combinatorial Giant
By Doron Zeilberger

Delivered Oct. 2, 2014

Videotaped lecture:

vimeo: part1 part2
youtube: part1 part2

[This lecture was delivered on Oct.2, 2014 at the Rutgers University Experimental Mathematics seminar organized by Matthew Russell and Doron Zeilberger.]

Dominique Foata's (b. Oct. 12, 1934) seminal contributions to Enumerative and Algebraic Combinatorics will be outlined in 48 minutes.
Acknowledgement: The video was filmed and uploaded to vimeo by Matthew Russell. It was uploaded to YouTube by Edinah Gnang.
Added Oct. 3, 2014: read Dominique Foata's interesting historical remarks

Maple package

FOATA, a Maple package that implements Dominique Foata's seminal bijective proof that sends the major index to the number of inversions (Proc. Amer. Math. Soc. 19(1968), 236-240, also briefly described in the "bible", Knuth's ACP3, 5.1.1, ex. 19)

Sample input and output

If you want to see a table of the clever Foata bijection for all permutations of length up to 7
The input yields the The output

If you want to see a verbose rendition of ONE (the first) recursive step, the Foata bijection for the permutation
6,2,7,1,10,11,3,5,4,8,12,9
The input yields the The output

If you want to see a super-verbose rendition of ALL the steps of the Foata bijection for the above permutation
The input yields the The output

If you want to see a table of the clever Foata bijection for all multi-set permutations of [1,1,1,2,2,2,3,3,3]
The input yields the The output

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