lexWeightsBetti -- a hash table containing the lex-leading weight Schur functors of a Veronese embedding

Synopsis

Usage:

lexWeightsBetti(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 lexicographically maximal weights of the Schur functors appearing in the Schur functor decomposition of $K_{p,q}(\mathbb{P}^n, d;b)$. 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 : lexWeightsBetti(3,2,0)

o2 = HashTable{(0, 0) => {0, 0, 0}}
               (0, 1) => {}
               (0, 2) => {}
               (1, 0) => {}
               (1, 1) => {4, 2, 0}
               (1, 2) => {}
               (2, 0) => {}
               (2, 1) => {6, 2, 1}
               (2, 2) => {}
               (3, 0) => {}
               (3, 1) => {7, 4, 1}
               (3, 2) => {}
               (4, 0) => {}
               (4, 1) => {8, 5, 2}
               (4, 2) => {}
               (5, 0) => {}
               (5, 1) => {9, 5, 4}
               (5, 2) => {}
               (6, 0) => {}
               (6, 1) => {9, 7, 5}
               (6, 2) => {}
               (7, 0) => {}
               (7, 1) => {}
               (7, 2) => {9, 9, 9}

o2 : HashTable

Ways to use lexWeightsBetti :

lexWeightsBetti(ZZ,ZZ,ZZ)

For the programmer

The object lexWeightsBetti is a method function.