dominantWeightsBetti -- a hash table containing the dominant Schur functors of a Veronese embedding

Synopsis

Usage:

dominantWeightsBetti(d,n,b)
Inputs:
- d, an integer,
- n, an integer,
- b, an integer,
Outputs:
- a hash table,

Description

This function returns a hash table $H$ whose keys are pairs $(p,q)$ such that the corresponding value $H#(p,q)$ is a list of the dominant weights appearing in the Schur functor decomposition of $K_{p,q}(\mathbb{P}^n, d;b)$. The Schur functors are recorded via the corresponding partitions. See Section 1.3 of [BEGY].

i1 : totalBettiTally(3,2,0)

            0  1   2   3   4   5  6 7
o1 = total: 1 27 105 189 189 105 27 1
         0: 1  .   .   .   .   .  . .
         1: . 27 105 189 189 105 27 .
         2: .  .   .   .   .   .  . 1

o1 : BettiTally

i2 : D = dominantWeightsBetti(3,2,0);

i3 : D#(1,1)

o3 = {{4, 2, 0}}

o3 : List

i4 : D#(5,1)

o4 = {{9, 5, 4}, {8, 7, 3}}

o4 : List

i5 : D#(7,2)

o5 = {{9, 9, 9}}

o5 : List

Ways to use dominantWeightsBetti :

dominantWeightsBetti(ZZ,ZZ,ZZ)

For the programmer

The object dominantWeightsBetti is a method function.