arXiv subjects

Sandor Radeleczki

Publications and source records attributed to Sandor Radeleczki.

4 recordsLinked to original sources

arXiv2026

On Boolean sublattices of finite partition lattices

We investigate maximal Boolean sublattices of the partition lattice Part(U) of a finite universe U. First, any largest size Boolean sublattice of Part(U) can be formed using all partitions whose blocks are subtrees of a tree with vertex set U. It is shown that a maximal Boolean sublattice of Part(U) always contains the least and the largest elements of Part(U). Boolean sublattices B of PartU containing 0 are characterized by a certain condition imposed on the cycles of a linear hypergraph corresponding to the atoms of B on the set U. We show that B can be extended to a Boolean sublattice of Part(U) with a largest size, if and only if the hypergraph induced by its atoms is a hypertree. This is the case when B is formed by all the partitions whose blocks are intervals in a generalized sense. The main result states that all partition lattices of height at least three have maximal Boolean sublattices for all possible dimensions at least three

math.CO↗

arXiv2020

Algebraic Approach to Directed Rough Sets

In relational approach to general rough sets, ideas of directed relations are supplemented with additional conditions for multiple algebraic approaches in this research paper. The relations are also specialized to representations of general parthood that are upper-directed, reflexive and antisymmetric for a better behaved groupoidal semantics over the set of roughly equivalent objects by the first author. Another distinct algebraic semantics over the set of approximations, and a new knowledge interpretation are also invented in this research by her. Because of minimal conditions imposed on the relations, neighborhood granulations are used in the construction of all approximations (granular and pointwise). Necessary and sufficient conditions for the lattice of local upper approximations to be completely distributive are proved by the second author. These results are related to formal concept analysis. Applications to student centered learning and decision making are also outlined.

cs.LO↗

arXiv2018

Involutive right-residuated l-groupoids

A common generalization of orthomodular lattices and residuated lattices is provided corresponding to bounded lattices with an involution and sectionally extensive mappings. It turns out that such a generalization can be based on integral right-residuated l-groupoids. This general framework is applied to MV-algebras,orthomodular lattices, Nelson algebras, basic algebras and Heyting algebras.

math.LO↗

arXiv2017

The meet operation in the imbalance lattice of maximal instantaneous codes: alternative proof of existence

An alternative proof is given of the existence of greatest lower bounds in the imbalance order of binary maximal instantaneous codes of a given size. These codes are viewed as maximal antichains of a given size in the infinite binary tree of 0-1 words. The proof proposed makes use of a single balancing operation instead of expansion and contraction as in the original proof of the existence of glb.

math.CO↗