Vol. 97, No. 2, 1981

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ISSN: 0030-8730
Polynomials in denumerable indeterminates

Richard Grassl

Vol. 97 (1981), No. 2, 415–423

D. Knuth used the Robinson-Schensted “insertion into a tableau” algorithm to give a direct 1-to-1 correspondence between “generalized permutations” and ordered pairs of generalized Young tableaux having the same shape. Since a generalized permutation characterizes a power product of differential indeterminates, the work of D. Mead on the principal differential ideal generated by a Wronskian provided an independent proof of the existence of the Knuth bijection. This work led Mead to suggest that other interesting combinatorial results may be found by equating the cardinalities of different vector space bases for the same finite-dimensional subspace of a differential ring. In a previous paper the author showed how such combinatorial identities follow from the study of “strong bases” for certain ideals in a ring of polynomials in a denumerable set of indeterminates. The present paper completes that work by presenting an infinite number of such strong bases and thus greatly expands the ring theory and differential algebra having applications in the enumeration of tableaux.

Mathematical Subject Classification 2000
Primary: 12H05
Secondary: 05A05
Received: 9 August 1977
Revised: 27 January 1981
Published: 1 December 1981
Richard Grassl