相关论文: A proof of Sendov's conjecture

New cases of the multiplicity conjecture are considered.

A generalization of the law of total covariance is presented and proved.

We give a counting based proof of the Graham Pollak Theorem

A combinatorial proof of the Gordon Conjecture: The sum of two Heegaard splittings is stabilized if and only if one of the two summands is stabilized.

A very short proof of Kneser's theorem via transversal is given.

We give a geometric proof of a conjecture of W. Fulton on the multiplicities of irreducible representations in a tensor product of irreducible representations for GL(r).

I prove Zamolodchikov's periodicity conjecture for type A with both ranks arbitrary.

In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…

We prove a recent conjecture of Sean A. Irvine about a nonlinear recurrence, using mechanized guessing and verification. The theorem-prover Walnut plays a large role in the proof.

In this note, we propose a conjecture stating that some series involving primitive sequences are convergent. Then, we show (by a counterexample) that the analogue of a conjecture of Erd\H{o}s, for those series, is false.

We prove Burkholder inequality using Bregman divergence.

We present an improved incremental selection algorithm of the selection algorithm presented in [1] and prove all the selected conjectures.

We present a short proof of Szemer\'edi's Theorem using a dynamical system enriched by ideas from model theory. The resulting proof contains features reminiscent of proofs based on both ergodic theory and on hypergraph regularity.

Using a result of Robertson \textit{[Proc. Edinburgh Math. Soc. (2), 1976]}, we introduce a notion of differentiation of maps on certain classes of unital commutative C*-algebras. We then derive C*-algebraic Gauss-Lucas theorem and…

We study a type of calculus for proving inequalities between subgraph densities which is based on Jensen's inequality for the logarithmic function. As a demonstration of the method we verify the conjecture of Erd\"os-Simonovits and…

We give a variational proof of the existence and uniqueness of a convex cap with the given upper boundary. The proof uses the concavity of the total scalar curvature functional on the space of generalized convex caps. As a byproduct, we…

We give a new proof of a_4\phi_3 summation due to G.E. Andrews and confirm another_4\phi_3 summation conjectured by him recently. Some variations of these two_4\phi_3 summations are also given.

We prove that a contractible orbifold is a manifold.

In this paper we prove the WALA conjecture.

In this work we resolve several conjectures stated in the On-Line Encyclopedia of Integer sequences.