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# makeBettiTally -- converts a hash table representing a Betti table to a Betti tally

## Synopsis

• Usage:
makeBettiTally(H)
• Inputs:
• H, ,
• Outputs:
• ,

## Description

Given a hash table $H$ whose keys are pairs of integers $(p,q)$ this function presents the data in the Betti tally format. For instance, combining this with the totalBetti function reproduces the standard Betti table. By contrast, combining this with the numRepsBetti function produces a table where the entry in position $(p,q)$ is the number of Schur functors in the representation corresponding to that Betti table entry.

 i1 : H = totalBetti(3,2,0); i2 : makeBettiTally H 0 1 2 3 4 5 6 7 o2 = total: 1 27 105 189 189 105 27 1 0: 1 . . . . . . . 1: . 27 105 189 189 105 27 . 2: . . . . . . . 1 o2 : BettiTally i3 : makeBettiTally numRepsBetti(3,2,0) 0 1 2 3 4 5 6 7 o3 = total: 1 1 4 7 7 4 1 1 0: 1 . . . . . . . 1: . 1 4 7 7 4 1 . 2: . . . . . . . 1 o3 : BettiTally

## Ways to use makeBettiTally :

• makeBettiTally(HashTable)

## For the programmer

The object makeBettiTally is .