An algebraic theory of sequence enumeration

Algebraic Enumeration

Enumeration of singular algebraic curves

We enumerate plane algebraic curves with one singular point of any (prescribed) singularity type. It is shown how to generalize the method to the singular hypersurfaces and some cases of enumeration of singular hypersurfaces are solved.

Sequence enumeration

The purpose of this paper is to present a method for treating uniformly a large number of enumeration problems involving sequences over a finite alphabet subject to general restrictions. Many of these problems are classical in origin, including the Mrnage problem (Lucas [16]), the alternating permutation problem (Netto [19], Andr6 [1, 2]), the derangement problem (Montmort [18]), and more recen...

Sequence Segmentation by Enumeration: An Exploration

We investigate exhaustive enumeration and subsequent language model evaluation (E&E approach) as an alternative to solving the sequence segmentation problem. We show that, under certain conditions (on string lengths and regarding a possibility to accurately estimate the number of segments), which are satisfied for important NLP applications, such as phonological segmentation, syllabification, a...

An Algebraic Representation of Graphs and Applications to Graph Enumeration

We give a recursion formula to generate all the equivalence classes of connected graphs with coefficients given by the inverses of the orders of their groups of automorphisms. We use an algebraic graph representation to apply the result to the enumeration of connected graphs, all of whose biconnected components have the same number of vertices and edges. The proof uses Abel’s binomial theorem a...