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Sticky polymatroids on at most five elements
Laszlo Csirmaz
The sticky polymatroid conjecture states that any two extensions of the polymatroid have an amalgam if and only if the polymatroid has no non-modular pairs of flats. We show that t…
Cyclic flats of a polymatroid
Laszlo Csirmaz
Polymatroids can be considered as "fractional matroid" where the rank function is not required to be integer valued. Many, but not every notion in matroid terminology translates na…
Sticky matroids and convolution
Laszlo Csirmaz
Motivated by the characterization of the lattice of cyclic flats of a matroid, the convolution of a ranked lattice and a discrete measure is defined, generalizing polymatroid convo…
Secret sharing and duality
Laszlo Csirmaz
Secret sharing is an important building block in cryptography. All explicitly defined secret sharing schemes with known exact complexity bounds are multi-linear, thus are closely r…
Complexity of universal access structures
Laszlo Csirmaz
An important parameter in a secret sharing scheme is the number of minimal qualified sets. Given this number, the universal access structure is the richest possible structure, name…
One-adhesive polymatroids
Laszlo Csirmaz
Adhesive polymatroids were defined by F. Matúš motivated by entropy functions. Two polymatroids are adhesive if they can be glued together along their joint part in a modular way;…