Stanley defines the fundamental bijection on page 30.
Given w=(14)(2)(375)(6), Stanley writes it in standard form (specifically: each cycle is written with its largest element first; cycles are written in increasing order of their largest element). Thus we obtain (2)(41)(6)(753).
Then we obtain w* from w by writing it in standard form an erasing the parentheses (that is, viewing the numbers as a word); here w* = 2416753.
Given this, w may be recoverd by inserting a left parenthesis preceding every lefttoright maximum, and right parentheses where appropriate.
1 2 3 4 5  standard(cyc,n=NULL)
standard_cyclist(x,n=NULL)
fbin_single(vec)
fbin(W)
fbin_inv(cyc)

vec 
In function 
W 
In functions 
cyc 
In functions 
n 
In function 
x 
In function 
The userfriendly functions are fbin()
and fbin_inv()
which perform Stanley's “fundamental bijection”. Function
fbin()
takes a word object and returns a cycle; function
fbin_inv()
takes a cycle and returns a word.
The other functions are lowlevel helper functions that are not really
intended for the user (except possibly standard()
, which puts a
cycle object in standard order in list form).
Robin K. S. Hankin
R. P. Stanley 2011 Enumerative Combinatorics
1 2 3 4 5 6 7 8 9 10 11 12 
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