Combinatorics inN=1Heterotic Vacua

Combinatorics Enumerative Combinatorics 05

Analytic Combinatorics — Symbolic Combinatorics

This booklet develops in nearly 200 pages the basics of combinatorial enumeration through an approach that revolves around generating functions. The major objects of interest here are words, trees, graphs, and permutations, which surface recurrently in all areas of discrete mathematics. The text presents the core of the theory with chapters on unlabelled enumeration and ordinary generating func...

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...

Generalized Flux Vacua

We consider type II string theory compactified on a symmetric T /Z2 orientifold. We study a general class of discrete deformations of the resulting fourdimensional supergravity theory, including gaugings arising from geometric and “nongeometric” fluxes, as well as the usual R-R and NS-NS fluxes. Solving the equations of motion associated with the resulting N = 1 superpotential, we find parametr...

Counting String/m Vacua

We report on some recent work with M. R. Douglas and B. Shiffman on vacuum statistics for flux compactifications in string/M theory.