Mathematically sound structures and fast algorithms for things around representation theory, especially algebraic Lie theory and accompanying combinatorics.
After a fruitless search for a good algorithm to generate all young tableaux of a given shape, I decided to write my own algorithm.
I am pretty happy with it's performance:
@benchmark semistandard_tableaux([4,3,2,1])
BenchmarkTools.Trial:
memory estimate: 1.53 GiB
allocs estimate: 12684703
--------------
minimum time: 2.148 s (21.97% GC)
median time: 2.413 s (31.98% GC)
mean time: 2.530 s (34.27% GC)
maximum time: 3.030 s (44.80% GC)
The main Contributor being
push!(SST, Tableau{T}(deepcopy(Tab)))
which adds the computated tableau to the output array.
Whithout this line, we can see that the rest of the algorithm contributes to less than 1% of the time it needs:
@benchmark semistandard_tableaux([4,3,2,1]) #without push!()
BenchmarkTools.Trial:
memory estimate: 1.11 KiB
allocs estimate: 11
--------------
minimum time: 9.334 ms (0.00% GC)
median time: 9.412 ms (0.00% GC)
mean time: 9.474 ms (0.00% GC)
maximum time: 12.053 ms (0.00% GC)
--------------
samples: 528
evals/sample: 1
For comparison, Sage took 29,4s for this computation.
I also implemented the schensted algorithm which might be handy at some point.
After a fruitless search for a good algorithm to generate all young tableaux of a given shape, I decided to write my own algorithm.
I am pretty happy with it's performance:
The main Contributor being
push!(SST, Tableau{T}(deepcopy(Tab)))which adds the computated tableau to the output array. Whithout this line, we can see that the rest of the algorithm contributes to less than 1% of the time it needs:For comparison, Sage took 29,4s for this computation.
I also implemented the schensted algorithm which might be handy at some point.