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Constraints on hypothetical counterexamples to the Casas-Alvero conjecture
Casas-Alvero conjecture polynomials Complex Variables
2012/4/18
The Casas-Alvero conjecture states: if a complex univariate polynomial has a common root with each of its derivatives, then it has a unique root. We show that hypothetical counterexamples must have at...
Counterexamples to a Monotonicity Conjecture for the Threshold Pebbling Number
combinatorics probability theory graph theory graph pebbling pebbling number pebbling threshold
2011/9/20
Abstract: Graph pebbling considers the problem of transforming configurations of discrete pebbles to certain target configurations on the vertices of a graph, using the so-called pebbling move. This p...
On the minimal set for counterexamples to the local-global principle
minimal set counterexamples local-global principle Number Theory
2011/9/14
Abstract: We prove that only for powers of 2 and 3 could occur counterexamples to the local-global divisibility principle for elliptic curves defined over the rationals. For we refine our previous cri...
Counterexamples to Ferromagnetic Ordering of Energy Levels
Heisenberg model quantum spin systems simple exclusion process ordering of energy levels Aldous ordering spectral gap
2011/8/26
Abstract: The Heisenberg ferromagnet has symmetry group ${\rm SU}(2)$. The property known as ferromagnetic ordering of energy levels (FOEL) states that the minimum energy eigenvalue among eigenvectors...
Quantum codes give counterexamples to the unique pre-image conjecture of the N-representability problem
Quantum codes give counterexamples the unique pre-image conjecture N-representability problem
2010/11/5
It is well known that the ground state energy of many-particle Hamiltonians involving only 2-body interactions can be obtained using constrained optimizations over density matrices which arise from r...
Family of counterexamples to King's conjecture
Family of counterexamples King's conjecture
2010/11/30
In this short note we present an infinite family of arbi-trary high dimensional ounterexamples to the King’s conjecture.