1,1

R. Bott, L. W. Tu, Differential forms in algebraic topology, New York: Springer, 1982.

Branko Malesevic, Some combinatorial aspects of differential operation composition on the space R^n, Univ. Beograd, Publ. Elektrotehn. Fak., Ser. Mat. 9 (1998), 29-33.

a(1) = number of meaningful differential operations of the 1st order on the space R^3 = 3 = A020701(1) namely {del_1, del_2, del_3} = {div, grad, curl}, since it is well-known that the 3 first-order differential operations on the space R^3 can be introduced using the operator of the exterior differentiation of differential forms [Bott].

a(2) = number of meaningful differential operations of the 2nd order on the space R^4 = A090989(2), namely 6 nontrivial second-order compositions del_j o del_k such that k + j = 4 + 1 and 2k not equal to 4.

a(3) = number of meaningful differential operations of the 3rd order on the space R^4 = 16 = A090990(3), namely 16 nontrivial third-order compositions del_k o del_j o del_k and del_j o del_k o del_j.

Main diagonal of A116183.

Cf. A020701, A090989-A090995, A129638, A129639.

Adjacent sequences: A127932 A127933 A127934 this_sequence A127936 A127937 A127938

Sequence in context: A013278 A009196 A116613 this_sequence A130596 A032247 A052281

nonn

Jonathan Vos Post (jvospost2(AT)yahoo.com), Apr 09 2007, Jun 08 2007