We show that an orientable pseudo-Anosov homeomorphism has vanishing SahArnoux-Fathi invariant if and only if the minimal polynomial of its dilatation is not reciprocal. We relate this to works of Margalit-Spallone and Birman, Brinkmann and Kawamuro. Mainly, we use Veech’s construction of pseudo-Anosov maps to give explicit pseudo-Anosov maps of vanishing Sah-Arnoux-Fathi invariant. In particul...

At this point, there are more additions than errors to report... 1.1. Pythagoras’ Constant. A geometric irrationality proof of √ 2 appears in [1] and a curious recursion is studied in [2]. More references on radical denestings include [3, 4, 5, 6]. 1.2. The Golden Mean. The cubic irrational χ = 1.8392867552... is mentioned elsewhere in the literature with regard to iterative functions [7, 8, 9]...

A hypergraph is a pair pV, Eq where V is a finite set and E Ď 2 is called the set of hyper-edges. An output-polynomial algorithm for C Ď 2 is an algorithm that lists without repetitions all the elements of C in time polynomial in the sum of the size of H and the accumulated size of all the elements in C. Whether there exists an output-polynomial algorithm to list all the inclusion-wise minimal ...

To make explicit computations with elliptic curves over finite fields, we need to know how to perform arithmetic operations in finite fields, and we would like to do so as efficiently as possible. In the applications we will consider, the finite fields involved may be very large, so it is important to understand the asymptotic complexity of finite field operations. This is a huge topic, one to ...

An output-polynomial algorithm for the listing of minimal dominating sets in graphs is a challenging open problem and is known to be equivalent to the well-known Transversal problem which asks for an output-polynomial algorithm for listing the set of minimal hitting sets in hypergraphs. We give a polynomial delay algorithm to list the set of minimal dominating sets in chordal graphs, an importa...

A fundamental part of a fault diagnosis system is the residual generator. Here a new method, the minimal polynomial basis approach, for design of residual generators for linear systems, is presented. The residual generation problem is transformed into a problem of finding polynomial bases for null-spaces of polynomial matrices. This is a standard problem in established linear systems theory, wh...

We reduce (in polynomial time) the enumeration of minimal dominating sets in interval and permutation graphs to the enumeration of paths in DAGs. As a consequence, we can enumerate in linear delay, after a polynomial time pre-processing, minimal dominating sets in interval and permutation graphs. We can also count them in polynomial time. This improves considerably upon previously known results...

A three-dimensional object has many possible representations inside a computer. Specifically, constructive solid geometry, boundary representation, and volumetric approximation techniques are commonly used to represent objects in solid geometric modeling (see [4]). Among the volumetric schemes are the octree [3] and the more recently developed switching-function representation [6] in which the ...

Minimal Polynomial Logic (MPL) is a generalisation of classical propositional logic which allows truth values in the continuous interval 0; 1] and in which propositions are represented by multi-variate polynomials. In previous work 7] we have introduced some properties of MPL and shown that it has two possible semantics: a) it can be considered as a logic for expressing, handling and computing ...

The easiest matrices to compute with are the diagonal ones. The sum and product of diagonal matrices can be computed componentwise along the main diagonal, and taking powers of a diagonal matrix is simple too. All the complications of matrix operations are gone when working only with diagonal matrices. If a matrix A is not diagonal but can be conjugated to a diagonal matrix, say D := PAP−1 is d...