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Let $s_d(n,N)$ be the number of different $d$-dimensional simplicial spheres on $n$ labelled vertices and $N$ facets (= $d$-simplices). I am in search for the best know upper bounds, especially for $d\...

I'd like to know how to enumerate and encode all (abstract) simplicial complexes of a given kind. To start as simple as possible, consider the familiy $\mathcal{S}_n^{d}$ of simplicial complexes which ...

By "a triangulation of $X$", I mean a simplicial complex whose geometric realization is homeomorphic to $X$. Tutte showed that the number of combinatorially distinct triangulations $t(n)$ of the $2$-...

Let $f_i$ be the number of $i$-dimensional faces in a $d$-dimensional simplicial complex $\Delta $. Recall that the $f$-vector of $\Delta $ is the vector $(f_{-1},f_0,f_1,\dots ,f_d)$ where $f_{-1}=...

Motivation: I am working on a problem that reduces to finding simplicial complexes given some data (details are unnecessary), but all I have managed to wrangle from my input is the number of cells of ...