相关论文: Suppressing nonrevisiting paths

The paper presents a counterexample to the Hodge conjecture.

We give a counterexample to a recently conjectured variant of the Penrose inequality.

We introduce the notion of a combinatorial inverse system in non-commutative variables. We present two important examples, some conjectures and results. These conjectures and results were suggested and supported by computer investigations.

In this paper, the abc conjecture is negated under certain conditions

In this paper we propose counterexamples to the Geometrization Conjecture and the Elliptization Conjecture.

In this paper, we extend the rectangular side of the shuffle conjecture by stating a rectangular analogue of the square paths conjecture. In addition, we describe a set of combinatorial objects and one statistic that are a first step…

In this paper, we give a simple counter example to the famous Hodge conjecture.

In this very short note, we give a counterexample to a recent conjecture of Gilmer which would have implied the union-closed conjecture.

We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.

A reinterpretation of noncommutativity as a mapping of paths is proposed at the level of quantum mechanics.

We prove that the intersection of a Hirsch polytope and a cube may be a non-Hirsch polytope.

In this note, we present a conjecture on intersections of set families, and a rephrasing of the conjecture in terms of principal downsets of Boolean lattices. The conjecture informally states that, whenever we can express the measure of a…

We prove a combinatorial reciprocity theorem for the enumeration of non-intersecting paths in a linearly growing sequence of acyclic planar networks. We explain two applications of this theorem: reciprocity for fans of bounded Dyck paths,…

We survey recent developments on the Restriction conjecture.

The article provides a counterexample to a conjecture by Blocki-Zwonek.

A short proof of the equivalence of the recurrence of non-backtracking random walk and that of simple random walk on regular infinite graphs is given. It is then shown how this proof can be extended in certain cases where the graph in…

This paper provides a new, decidable definition of the higher- order recursive path ordering in which type comparisons are made only when needed, therefore eliminating the need for the computability clo- sure, and bound variables are…

When a proposition has no proof in an inference system, it is sometimes useful to build a counter-proof explaining, step by step, the reason of this non-provability. In general, this counter-proof is a (possibly) infinite co-inductive proof…

We survey the state of the union-closed sets conjecture.

In this note we investigate the Cheltsov--Rubinstein conjecture. We show that this conjecture does not hold in general and some counterexamples will be presented.