Counterexamples to Q-matrix conjectures

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 the Poset Conjectures of Neggers, Stanley, and Stembridge

We provide the first counterexamples to Neggers’ 1978 conjecture and Stembridge’s 1997 conjecture that the generating functions for descents and peaks in the linear extensions of naturally labeled posets should have all real zeros. We also provide minimum-sized counterexamples to a generalization of the Neggers conjecture due to Stanley that was recently disproved by Brändén.