We give a new proof of the Skeletal Lemma, which is main technical tool in our paper on Hamilton cycles line graphs (Kaiser and Vrána, 2012). It generalises results disjoint spanning trees to context 3-hypergraphs. The lemma proved slightly stronger version that more suitable for applications. simplified formulated accessible way.

To an extended generalized permutohedron we associate the weighted integer points enumerator, whose principal specialization is f-polynomial. In case of poset cones it refines Gessel?s P-partitions enumerator. We show that this enumerator a quasisymmetric function obtained by universal morphism from Hopf algebra posets.

Abstract Inequalities are important features in the context of sequences numbers and polynomials. The Bessenrodt–Ono inequality for partition Nekrasov–Okounkov polynomials has only recently been discovered. In this paper we study log-concavity (Turán inequality) plane partitions their polynomization.

The rules of “Bulgarian solitaire” are considered as an operation on the set of partitions to induce a finite dynamical system. We focus on partitions with no preimage under this operation, known as Garden of Eden points, and their relation to the partitions that are in cycles. These are the partitions of interest, as we show that starting from the Garden of Eden points leads through the entire...

this paper firstly generalizes majority vote to fuzzy majority vote, then proposes a cluster matching algorithm that is able to establish correspondence among fuzzy clusters from different fuzzy partitions over a common data set. Finally a new combination model of fuzzy partitions is build on the basis of the proposed cluster matching algorithm and fuzzy majority vote. Comparative results show ...

We consider the problem of partitioning the vertex-set of a tree to p parts to minimize a cost function. Since the number of partitions is exponential in the number of vertices, it is helpful to identify small classes of partitions which also contain optimal partitions. Two such classes, called consecutive partitions and nested partitions, have been well studied for the set partition problem, w...