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

## Synopsis

• Usage:
lexWeightsBetti(d,n,b)
• Inputs:
• Outputs:
• ,

## 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 .