PART::Part2ListHook --
calculates the list of hook lengths
Call(s)
PART::Part2ListHook(part)
Parameterspart | - | any list denoting a partition |
Introduction
The PART::Part2ListHook function computes the list of all hook lengths of a
given partition.
The result is sorted into non-increasing order.
The arm and leg length of a cell (i,j) are respectively
part[i] - j and cpart[j] - i
where cpart is the conjugate of part.
The call computes the Jack-hook-product.
PART::Part2ListHook(part,a)a may be any expression.
This is the product
a*arm_length[i,j] + leg_length[i,j] + 1
over all cells of the diagram of the partition part.
The call computes the two-variable hook
polynomial.
The arguments PART::Part2ListHook(part,q,t)q and t can be any expressions.
This is the product
1 - q^arm_length[i,j] x t^(1+leg_length[i,j])
over all cells of the diagram of the partition part.
Example 1>> muEC::PART::Part2ListHook( [3,1] );
[4, 2, 1, 1]
>> 4! / _mult( op(%) );
3
>> muEC::PART::Part2ListHook( [2,1], z );
z + 2
>> muEC::PART::Part2ListHook( [2,1], z, t );
2 2
- (t z - 1) (t - 1)
Related FunctionsPart2Conjugate, Part2Border, Part2Diagonal, Part2Mat, ListPart, TYP::IsPart
MuPAD Combinat, an open source algebraic combinatorics package