TOPICS

# Bumping Algorithm

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.

Tableau Class, Young Tableau

## Explore with Wolfram|Alpha

More things to try:

## References

Skiena, S. Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, 1990.

## Referenced on Wolfram|Alpha

Bumping Algorithm

## Cite this as:

Weisstein, Eric W. "Bumping Algorithm." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BumpingAlgorithm.html