5 papers
Orchards in elliptic curves over finite fields
R. Padmanabhan, Alok Shukla
Consider a set of points on a plane. A line containing exactly out of the points is called a -rich line. The classical orchard problem asks for a configurati…
When do we have 1 + 1 = 11 and 2 + 2 =5?
R. Padmanabhan, Alok Shukla
The phrase "" is a cliché or a slogan used in political speeches, propaganda, or literature, most notably in the novel "" by George Orwell. More recently, we came…
Means Compatible with Semigroup Laws
R. Padmanabhan, Alok Shukla
A binary mean operation m(x,y) is said to be compatible with a semigroup law *, if * satisfies the Gauss' functional equation m(x,y) * m(x,y) = x * y for all x, y. Thus the arithme…
A 2-base for inverse semigroups
Joao Araujo, Michael Kinyon, R. Padmanabhan
An open problem in the theory of inverse semigroups was whether the variety of such semigroups, when viewed as algebras with a binary operation and a unary operation, is 2-based, t…
Yet Another Single Law for Lattices
William McCune, Ranganathan Padmanabhan, Robert Veroff
In this note we show that the equational theory of all lattices is defined by a single absorption law. The identity of length 29 with 8 variables is shorter than previously known s…