35 citations · 85 across the 9 of their papers we have counts for
10 papers
The Tight Upper Bound for the Size of Single Deletion Error Correcting Codes in Dimension 11
Kazuhisa Nakasho, Manabu Hagiwara, Austin Anderson +1
A single deletion error correcting code (SDECC) is a set of fixed-length sequences consisting of two types of symbols, 0 and 1, such that the original sequence can be recovered for…
Planar, infinite, semidistributive lattices
George Grätzer, J. B. Nation
An FN lattice is a simple, infinite, semidistributive lattice. Its existence was recently proved by R. Freese and J.\,B. Nation. Let denote the Boolean lattice w…
The Bases of Association Rules of High Confidence
Oren Segal, Justin Cabot-Miller, Kira Adaricheva +2
We develop a new approach for distributed computing of the association rules of high confidence in a binary table. It is derived from the D-basis algorithm in K. Adaricheva and J.B…
Discovery of the -basis in binary tables based on hypergraph dualization
Kira Adaricheva, J. B. Nation
Discovery of (strong) association rules, or implications, is an important task in data management, and it finds application in artificial intelligence, data mining and the semantic…
A class of infinite convex geometries
Kira Adaricheva, J. B. Nation
Various characterizations of finite convex geometries are well known. This note provides similar characterizations for possibly infinite convex geometries whose lattice of closed s…
Group Coding with Complex Isometries
Hye Jung Kim, J. B. Nation, Anne V. Shepler
We investigate group coding for arbitrary finite groups acting linearly on a vector space. These yield robust codes based on real or complex matrix groups. We give necessary and su…
On implicational bases of closure systems with unique critical sets
Kira Adaricheva, J. B. Nation
We show that every optimum basis of a finite closure system, in D.Maier's sense, is also right-side optimum, which is a parameter of a minimum CNF representation of a Horn Boolean…
Ordered direct implicational basis of a finite closure system
Kira Adaricheva, J. B. Nation, Robert Rand
Closure system on a finite set is a unifying concept in logic programming, relational data bases and knowledge systems. It can also be presented in the terms of finite lattices, an…
Lattices of quasi-equational theories as congruence lattices of semilattices with operators, Part II
Kira Adaricheva, J. B. Nation
Part I proved that for every quasivariety K of structures (which may have both operations and relations) there is a semilattice S with operators such that he lattice of quasi-equat…
Lattices of quasi-equational theories as congruence lattices of semilattices with operators, Part I
Kira Adaricheva, J. B. Nation
We show that for every quasivariety K of structures (where both functions and relations are allowed) there is a semilattice S with operators such that the lattice of quasi-equation…