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# bsCoeffs -- a list of the Boij-Soederberg coefficients of a Veronese embedding

## Description

This function returns a list of the Boij-Soederberg coefficients for the decomposition of the Betti table of $\mathcal{O}(b)$ on $\mathbb{P}^{n}$ under the $d$-fold Veronese embedding. See Section 6.3 of [BEGY]. Of course, these coefficients and the corresponding pure diagrams are easily computed by applying decompose(BettiTally) from the BoijSoederberg package to the corresponding totalBettiTally.

 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 : bsCoeffs(3,2,0) o2 = {45360} o2 : List i3 : totalBettiTally(4,2,2) 0 1 2 3 4 5 6 7 8 9 10 11 12 o3 = total: 6 62 276 715 1275 2628 4488 4950 3630 1804 588 114 10 0: 6 62 276 660 825 252 . . . . . . . 1: . . . 55 450 2376 4488 4950 3630 1804 588 114 10 2: . . . . . . . . . . . . . o3 : BettiTally i4 : bsCoeffs(4,2,2) o4 = {1219276800, 4746470400, 1219276800, 479001600} o4 : List

## Ways to use bsCoeffs :

• bsCoeffs(ZZ,ZZ,ZZ)

## For the programmer

The object bsCoeffs is .