Related papers: Proof of Han's Hook Expansion Conjecture

In a recent paper, Park and Pham famously proved Kahn-Kalai conjecture. In this note, we simplify their proof, using an induction to replace the original analysis. This reduces the proof to one page, and from the argument it is also easy to…

We prove two single-parameter q-supercongruences which were recently conjectured by Guo, and establish their further extensions with one more parameter. Crucial ingredients in the proof are the terminating form of q-binomial theorem and a…

In this paper the circulant Hadamard conjecture is proved.

Recently, a new weighted generalization of the branching rule for the hook lengths, equivalent to the hook formula, was proved. In this paper, we generalize the complementary branching rule, which can be used to prove Burnside's formula. We…

The Nekrasov--Okounkov hook length formula provides a fundamental link between the theory of partitions and the coefficients of powers of the Dedekind eta function. In this paper we examine three conjectures presented by Amdeberhan. The…

Beginning from the resolution of the Dirichlet L function, using the inner product formula between two infinite-dimensional vectors in the complex space, the author proved the baffling problem--Hecke conjecture.

Recently, Naruse presented a beautiful cancellation-free hook-length formula for skew shapes. The formula involves a sum over objects called excited diagrams, and the term corresponding to each excited diagram has hook lengths in the…

Recently Z.W.Sun found over hundred conjectured formulas for 1/pi. Many of them were proved by H.H.Chan, J.Wan andW.Zudilin (see [3], [8] in the paper). Here we show that several other formulas in [6] are simple transformations of known…

We prove the Aharoni Berger Conjecture

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

We survey recent developments on the Restriction conjecture.

In [1], Theorem 3, the authors proved, in one dimension, a generalization of the Hopf Lemma, and the question arose if it could be extended to higher dimensions. In this paper we present two conjectures as possible extensions, and give a…

The said paper [2] entitled "Proof Of Two Dimensional Jacobian Conjecture" is with gaps.

We prove the Gan-Gross-Prasad conjecture for $\left(\mathrm{U}\left(2n\right),\mathrm{U}\left(1\right)\right)$ in general and prove its refinement, namely the Ichino-Ikeda type explicit formula for the central $L$-values, under certain…

We formulate a precise conjecture that, if true, extends the converse theorem of Hecke without requiring hypotheses on twists by Dirichlet characters or an Euler product. The main idea is to linearize the Euler product, replacing it by…

We give a Newton type rational interpolation formula (Theorem \ref{theo}). It contains as a special case the original Newton interpolation, as well as the recent interpolation formula of Zhi-Guo Liu, which allows to recover many important…

Han recently discovered new hook length identities for binary trees. In this paper, we extend Han's identities to binomial families of trees. Moreover, we present a bijective proof of one of the identities for the family of ordered trees.

We establish the exact overlaps conjecture for iterated functions systems on the real line with algebraic contractions and arbitrary translations.

For Fatou's interpolation theorem of 1906 we suggest a new elementary proof.

A conjecture regarding the structure of expander graphs is discussed.