Opened 6 years ago

# Two algorithms for k-charge do not give same answer — at Version 4

Reported by: Owned by: aschilling major sage-6.1 combinatorics tableaux, charge sage-combinat, zabrocki Anne Schilling N/A public/combinat/k-charge-15444 (Commits) 8df647454982f5799a4267712551a78989f08992

Currently, the two implementations of k-charge do not give the same answer:

```sage: T = WeakTableaux(4,[4,3,2,1],[2,2,2,2,1,1],representation='bounded')
sage: for t in T:
print t.k_charge(), t.k_charge(algorithm='J')
....:
9 10
10 10
8 8
9 9
10 10
8 9
11 11
```

Comparing against the expansion of Hall-Littlewood symmetric functions in terms of k-Schur functions, it seems that the I-implementation is correct

```sage: Sym = SymmetricFunctions(QQ['t'])
sage: Qp = Sym.hall_littlewood().Qp()
sage: ks = Sym.kschur(4)
sage: ks(Qp[2,2,2,2,1,1])[Partition([4,3,2,1])]
t^11 + 2*t^10 + 2*t^9 + 2*t^8
```

Compared to the book http://arxiv.org/abs/1301.3569 pg. 84 the bug seems to be in the method _height_of_restricted_subword in k_tableau.py.

### comment:1 follow-up: ↓ 2 Changed 6 years ago by zabrocki

Proposition 3.15 on p. 84 of our book states that the k-charge with the two algorithms are equal. Am I correct to assume that since you opened a ticket that the error is in the algorithm and not in that proposition?

To clarify

```sage: T = WeakTableau([[1, 1, 2, 3], [2, 4, 4], [3, 6], [5]],4,representation='bounded')
sage: T.k_charge()
9
sage: T.k_charge(algorithm='J')
10
```

### comment:2 in reply to: ↑ 1 Changed 6 years ago by aschilling

Yes, I think the implementation that Avi and Nate did is not quite correct. If you look at the second standard subword of your example above, then the program computes the height of the restricted subword incorrectly for the letter r=3.

### comment:3 Changed 6 years ago by aschilling

• Authors set to Anne Schilling
• Branch set to public/combinat/k-charge-15444
• Commit set to 8df647454982f5799a4267712551a78989f08992
• Status changed from new to needs_review

New commits:

 ​8df6474 Fixed bug in k-charge implementation for J-algorithm

### comment:4 Changed 6 years ago by aschilling

• Description modified (diff)
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