Pascal-like determinants are recursive

A Pascal-like Triangle Related to the Tribonacci Numbers

A tile composed of two pieces, which we refer to as a fence tile, is introduced to give the Tribonacci numbers a new combinatorial interpretation. The interpretation is used to construct a Pascal-like triangle and various identities concerning the triangle are proven. An intuitive proof of a general identity for the Tribonacci numbers in terms of sums of products of the binomial coefficients is...

Intron Length and Recursive Sites Are Major Determinants of Splicing Efficiency in Flies

Primitive Recursive Bars Are Inductive

Using Martín Escardó’s « effectful forcing » technique, we demonstrate the constructive validity of Brouwer’s monotone Bar Theorem for any System T-definable bar. We have not assumed any non-constructive (Classical or Brouwerian) principles in this proof, and have carried out the entire development formally in the Agda proof assistant [13] for Martin-Löf ’s Constructive TypeTheory. In 2013, Mar...

Vector Pascal

Vector Pascal is a language designed to support elegant and efficient expression of algorithms using the SIMD model of computation. It imports into Pascal features derived from the functional languages APL and J, in particular the extension of all operators to work on vectors of data. The type system is extended to handle dimensional analysis. Code generation is via the ILCG system that allows ...

Pascal Matrices

Every polynomial of degree n has n roots; every continuous function on [0, 1] attains its maximum; every real symmetric matrix has a complete set of orthonormal eigenvectors. “General theorems” are a big part of the mathematics we know. We can hardly resist the urge to generalize further! Remove hypotheses, make the theorem tighter and more difficult, include more functions, move into Hilbert s...