Manuscript XVI-K@1 · XVI-K.tex · section · aa7553bb

Homogeneity, inventory, and the finite graded span

Homogeneity, inventory, and the finite graded span · lines 1032–1062

Type	Unordered	Ordered	Degree	$N_{k}$	Residual jet
$S^{2}$	1	1	$- 4$	0	$\partial^{2} h$
$S \partial_{α} S$	4	8	$- 5$	1	$\partial h$
$\partial_{α} S \partial_{β} S$	10	16	$- 6$	2	$h$
$S \partial_{α} \partial_{β} S$	10	20	$- 6$	2	$h$
Total	25	45

The cardinalities count allowable placements. The supplied computational record further reports that every ordered placement has a nonzero Hessian coefficient; that stronger occurrence statement is not needed for the analytic bound.

No numerical kernel has more than two vertex derivatives. The preparation jet $Σ (y)$ stays in the coefficient and contributes no additional edge derivative.

Nearby in this section

section: Homogeneity, inventory, and the finite graded span
lemma: Lemma: Homogeneity from the Fourier families
proposition: Proposition: Numerical scaling and declared subtraction orders
lemma: Lemma: Grading and punctured identities
section: Homogeneity, inventory, and the finite graded span