Franklin's argument proves an identity of Zagier.
An infinite family of dual sequence identities.
On a septuple product identity.
A new proof of some identities of Bressoud.
Lagrange inversion and Stirling number convolutions.
A conjecture of Stanley on alternating permutations.
Reciprocity laws for generalized higher dimensional Dedekind sums
We define a class of generalized Dedekind sums and prove a family of reciprocity laws for them. These sums and laws generalize those of Zagier [6]. The method is based on that of Solomon [5].
Determinants of Legendre symbol matrices
Universal codes and unimodular lattices
Binary quadratic residue codes of length produce via construction and density doubling type II lattices like the Leech. Recently, quaternary quadratic residue codes have been shown to produce the same lattices by construction modulo . We prove in a direct way the equivalence of these two constructions for . In dimension 32, we obtain an extremal lattice of type II not isometric to the Barnes-Wall lattice . The equivalence between construction modulo plus density doubling and construction...
-modular lattices from ternary codes
The alphabet where is viewed here as a quotient of the ring of integers of by the ideal (3). Self-dual codes for the hermitian scalar product give -modular lattices by construction . There is a Gray map which maps self-dual codes for the Euclidean scalar product into Type III codes with a fixed point free involution in their automorphism group. Gleason type theorems for the symmetrized weight enumerators of Euclidean self-dual codes and the length weight enumerator of hermitian self-dual...
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