Mark C. Wilson

Asymptotics of Multivariate Sequences II: Multiple Points of the Singular Variety

Let

Twenty Combinatorial Examples of Asymptotics Derived from Multivariate Generating Functions

F(\b{z})=\sum_\b{r} a_\b{r}\b{z^r}

Asymptotics of Multivariate Sequences

be a multivariate generating function that is meromorphic in some neighbourhood of the origin of

Exact results on manipulability of positional voting rules

\mathbb{C}^d

Compound constructions of broadcast networks

, and let

Best reply dynamics for scoring rules

\sing

Asymptotics of the minimum manipulating coalition size for positional voting rules under impartial culture behaviour

be its set of singularities. Effective asymptotic expansions for the coefficients can be obtained by complex contour integration near points of

Associative algebras satisfying a semigroup identity

\sing

Group algebras and enveloping algebras with nonmatrix and semigroup identities

.In the first article in this series, we treated the case of smooth points of

The complexity of safe manipulation under scoring rules

\sing