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

Synopsis

Usage:

bsCoeffs(d,n,b)
Inputs:
- d, an integer,
- n, an integer,
- b, an integer,
Outputs:
- a list,

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 a method function.