English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Recently we introduced the hypergraph matrix model (HMM), a Hermitian matrixmodel generalizing the classical Gaussian Unitary Ensemble (GUE). In this modelthe Gaussians of the GUE, whose moments count partitions of finite sets intopairs, are replaced by formal measures whose moments count set partitions intoparts of a fixed even size 2m >= 2. Just as the expectations of the tracepolynomials Tr X^{2r} in the GUE produce polynomials counting unicellularorientable maps of different genera, in the HHM these expectations givepolynomials counting certain unicelled edge-ramified CW complexes with extradata that we call (orientable CW) maps with instructions. In this paper wedescribe generating functions for maps with instructions of fixed genus andwith the number of vertices arbitrary. Our results are motivated by work ofWright. In particular Wright computed generating functions of connected graphsof fixed first Betti number as rational functions in the rooted tree function T(x), given as the solution to the functional relation x = T e^{-T}.

Hypergraph matrix models and generating functions