[seqfan] Re: Generating the symmetric group with minimal products of involutions

Richard J. Mathar mathar at mpia-hd.mpg.de
Wed Jan 4 14:36:38 CET 2017


In response to http://list.seqfan.eu/pipermail/seqfan/2016-December/017171.html
I figured out that each element of order >=3 of the symmetric group S_n can be written
as a product of 2 involutions. I added an associated comment to A066052 showing
that permutations of order >=3 can be written as a product of 2 involutions. I did
not submit the associated array mentioned in http://list.seqfan.eu/pipermail/seqfan/2016-December/017168.html
because that would be trivially limited to
T(n,0)=1
T(n,1)=A001189(n), n>=2.
T(n,2)=A066052(n), n>=3.
with row sums A000142(n).



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