We prove the results about mixed Buchsbaumâ€“Rim multiplicities announced in [6, (9.10)(ii), p. 224], including a general mixed-multiplicity formula. In addition, we identify these multiplicities as the coefficients of the " leading form " of the appropriate Buchsbaum-Rim polynomial in three variables, and we prove a positivity theorem. In fact, we define theâ€¦ (More)

For a given set of real weights, Huffman trees minimize the weighted external path length. Over the years, several algorithms have been proposed for constructing Huffman trees that minimize additional natural cost functions such as the external path length, the variance and, more generally, the central moments. We show that all these cost functions areâ€¦ (More)

Let A be a Noetherian local domain, N be a finitely generated torsion-free module, and M a proper submodule that is generically equal to N . Let A[N ] be an arbitrary graded overdomain of A generated as an A-algebra by N placed in degree 1. Let A[M ] be the subalgebra generated by M . Set C := Proj(A[M ]) and r := dimC. Form the (closed) subset W of Spec(A)â€¦ (More)

For a given monic polynomial p(t) of degree n over a commutative ring k, the splitting algebra is the universal k-algebra in which p(t) has n roots, or, more precisely, over which p(t) factors, p(t) = (t âˆ’ Î¾1) Â· Â· Â· (t âˆ’ Î¾n). The symmetric group Sr for 1 â‰¤ r â‰¤ n acts on the splitting algebra by permuting the first r roots Î¾1, . . . , Î¾r . We give a natural,â€¦ (More)