Given a permutation 
of 
, the bumping algorithm constructs a standard Young
tableau by inserting the 
one by one into an already constructed Young
tableau. To apply the bumping algorithm, start with 
, which is a Young tableau.
If 
through 
have already been inserted, then in order to insert 
, start with the first line of the already constructed
Young tableau and search for the first element of
this line which is greater than 
. If there is no such element, append 
to the first line and stop. If there is such an element
(say, 
),
exchange 
for 
,
search the second line using 
, and so on.
Bumping Algorithm
See also
Tableau Class, Young TableauExplore with Wolfram|Alpha
References
Skiena, S. Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, 1990.Referenced on Wolfram|Alpha
Bumping AlgorithmCite this as:
Weisstein, Eric W. "Bumping Algorithm." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BumpingAlgorithm.html