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

- 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.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/SchurVeronese/doc.m2:242:0.