Counterexamples to two conjectures about distance sequences

Counterexamples to witness conjectures

Consider the class of exp-log constants, which is constructed from the integers using the field operations, exponentiation and logarithm. Let z be such an exp-log constant and let n be its size as an expression. Witness conjectures attempt to give bounds $(n) for the number of decimal digits which need to be evaluated in order to test whether z equals zero. For this purpose, it is convenient to...

Counterexamples to Indexing System Conjectures

Chaotic Polynomial Automorphisms; counterexamples to several conjectures

We give a polynomial counterexample to a discrete version of the Markus-Yamabe Conjecture and a conjecture of Deng, Meisters and Zampieri, asserting that if F : C → C is a polynomial map with det(JF ) ∈ C∗, then for all λ ∈ R large enough λF is global analytic linearizable. These counterexamples hold in any dimension ≥ 4.

Counterexamples to three conjectures concerning perfect graphs

We will present counterexamples to a conjecture of Hoàng, a conjecture of Hertz and de Werra and to a conjecture of Reed. All these three conjectures are related to perfect graphs.

Counterexamples to conjectures about Subset Takeaway and counting linear extensions of a Boolean lattice

We develop an algorithm for efficiently computing recursively defined functions on posets. We illustrate this algorithm by disproving conjectures about the game Subset Takeaway (Chomp on a hypercube) and computing the number of linear extensions of the lattice of a 7-cube and related lattices.