40 citations · 64 across the 27 of their papers we have counts for
11 papers · 1 filter
Enumerating all minimal hitting sets in polynomial total time
Marcel Wild
Consider a hypergraph (=set system) whose hyperedges are subsets of a set with w elements. We show that the minimal hitting sets of can be enumera…
Modular lattices of finite length (Part A)
Marcel Wild
This is Part A of four Parts dedicated to modular lattices of finite length. It builds on 1992 notes of the author (available on ResearchGate), and in so doing heeds a wish of the…
Compression with wildcards: All exact, or all minimal hitting sets
Marcel Wild
Our main objective is the COMPRESSED enumeration (based on wildcards) of all minimal hitting sets of general hypergraphs. To the author's best knowledge the only previous attempt t…
Finding or counting all shellings of a simplicial complex
Marcel Wild
The shellability status of previously investigated simplicial complexes with up to 24 facets is settled. In case of shellability the exact number of shellings is determined. Our al…
Tight embedding of modular lattices into partition lattices: progress and program
Marcel Wild
Representing lattices L by equivalence relations amounts to embed them into the lattice Part(V) of all partitions of a set V, and has a long history. Here we are concerned with MOD…
How to partition or count an abstract simplicial complex, given its facets
Marcel Wild
Given are the facets of an abstract (finite) simplicial complex SC. We show how to partition SC into few pieces, each one compactly encoded by the use of wildcards. Such a represen…
Output polynomial enumeration of all fixed-cardinality ideals of a poset, respectively all fixed-cardinality subtrees of a tree
Marcel Wild
The N cardinality k ideals of any w-element poset (w, k variable) can be enumerated in time O(Nw^3). The corresponding bound for k-element subtrees of a w-element tree is O(Nw^5).…
A catalogue of small regular matroids and their Tutte polynomials
Harald Fripertinger, Marcel Wild
A catalogue of all non-isomorphic simple connected regular matroids of cardinality is provided on the net. These matroids are given as binary matrix matroids…
Lattices freely generated by posets within a variety. Part II: Finitely generated varieties
Jean Yves Semegni, Marcel Wild
This article is the second part of an essay dedicated to lattices freely generated by posets within a variety. The first part dealt with four easy varieties while this part is conc…
Lattices freely generated by posets within a variety. Part I: Four easy varieties
Jean Yves Semegni, Marcel Wild
We introduce an algorithm for computing closure systems derived from a family of implications on a set. Semilattices presentations are explored and used in conjunction with the alg…
Realization of abstract convex geometries by point configurations, Part 1
Kira Adaricheva, Marcel Wild
The Edelman-Jamison problem is to characterize those abstract convex geometries that are representable by a set of points in the plane. We show that some natural modification of th…