18 citations · 19 across the 8 of their papers we have counts for
9 papers
Blocks in Finite Hyperfields
David Hobby
This paper studies the structure of finite hyperfields , and finds a subtle pattern in their addition operation. Consider the class of all hyperfields with a given…
Nontrivial solutions for homogeneous linear equations over some non-quotient hyperfields
David Hobby, Jaiung Jun
We introduce a class of hyperfields which includes several constructions of non-quotient hyperfields. We then use it to partially answer a question posed by M. Baker and T. Zhang:…
Laplace invariants of differential operators
David Hobby, Ekaterina Shemyakova
We identify conditions giving large natural classes of partial differential operators for which it is possible to construct a complete set of Laplace invariants. In order to do tha…
Sums of finitely many distinct rationals
Donald Silberger, Sylvia Silberger, David Hobby
denotes the family of all finite nonempty , and when . Simila…
Classification of Multidimensional Darboux Transformations: First Order and Continued Type
David Hobby, Ekaterina Shemyakova
We analyze Darboux transformations in very general settings for multidimensional linear partial differential operators. We consider all known types of Darboux transformations, and…
Term inequalities in finite algebras
David Hobby
Given an algebra , and terms and of the language of , we say that and are {\em separated}…
Roots with common tails
Alexandra Hobby, David Hobby
Some cubic polynomials over the integers have three distinct real roots with continued fractions that all have the same common tail. We characterize the polynomials for which this…
Antiassociative Groupoids
Milton Braitt, David Hobby, Donald Silberger
Given a groupoid , and , we say that is antiassociative iff for all , and a…
Completely dissociative groupoids
Milton S. Braitt, David Hobby, Donald Silberger
Consider arbitrarily parenthesized expressions on the variables , where each appears exactly once and in the order of their indices. We call these…