Incidence combinatorics of resolutions

Incidence Combinatorics

We introduce notions of combinatorial blowups, building sets, and nested sets for arbitrary meet-semilattices. This gives a common abstract framework for the incidence combinatorics occurring in the context of De Concini-Procesi models of subspace arrangements and resolutions of singularities in toric varieties. Our main theorem states that a sequence of combinatorial blowups, prescribed by a b...

Combinatorics on Adjacency Graphs and Incidence Pseudographs

The paper starts with a brief review of combinatorial results for adjacency and oriented adjacency graphs (combinatorial maps). The main subject is incidence pseudographs (a dual of cell complexes) of the n-dimensional orthogonal grid. It is well known that these pseudographs (or complexes) allow a definition of a topological space, and combinatorial formulas are provided for characterizing ope...

Combinatorics of Sphere Covers and the Shift-Incidence Matrix

Most problems in algebra, at some stage, must consider algebraic equations. Sometimes solving them, other times producing them – so their existence manifests a desired structure. Akin to doing differential equations, a researcher in algebraic equations must specialize to get somewhere. My speciality is algebraic equations in two variables, say w and z, where one variable, say z, interprets as a...

The Order Steps of an Analytic Combinatorics

‎Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures‎. ‎This theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines‎, ‎including probability theory‎, ‎statistical physics‎, ‎computational biology and information theory‎. ‎With a caref...

Combinatorics Enumerative Combinatorics 05