PART::Part2ListHook
--
calculates the list of hook lengths
PART::Part2ListHook(part)
part | - | any list denoting a partition |
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.
>> 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)
Part2Conjugate
, Part2Border
, Part2Diagonal
, Part2Mat
, ListPart
, TYP::IsPart
MuPAD Combinat, an open source algebraic combinatorics package