相关论文: Congruences for Broken k-Diamond Partitions

We present a summary of the latest measurements of branching fractions and direct CP violations in the charmless hadronic two-body B decays B -> K^+ pi^-, K^+ pi^0, K^0 pi^+ and K^0 pi^0, performed by the Belle, BABAR, CDF and CLEO…

We prove two polynomial identities which are particular cases of a conjecture arising in the theory of L-functions of twisted Carlitz modules. This conjecture is stated in earlier papers of the second author.

Results are well-known

Motivated by physics, we propose two conjectures regarding the cohomology ring of the crepant resolutions of orbifolds and cohomological invariants of K-equivalent manifolds.

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.

New identities and congruences involving the ranks and cranks of partitions are proved. The proof depends on a new partial differential equation connecting their generating functions.

Euclidean billiard partitions were recently introduced by Andrews, Dragovic and Radnovic in their study of periodic trajectories of ellipsoidal billiards in the Euclidean space. They are integer partitions into distinct parts such that (E1)…

We establish the consistency of the failure of the diamond principle on a cardinal $\kappa$ which satisfies a strong simultaneous reflection property. The result is based on an analysis of Radin forcing, and further leads to a…

We prove two conjectures in this paper. The first conjecture is by Lund, Pham and Thu: Given a Borel set $A\subset \mathbb{R}^n$ such that $\dim A\in (k,k+1]$ for some $k\in\{1,\dots,n-1\}$. For $0<s<k$, we have \[ \text{dim}(\{y\in…

The classical honeycomb conjecture asserts that any partition of the plane into regions of equal area has perimeter at least that of the regular hexagonal honeycomb tiling. Pappus discusses this problem in his preface to Book V. This paper…

We show that it is consistent that the Borel Conjecture and the dual Borel Conjecture hold simultaneously.

We present a detailed comparison of the structural predictions of the effective many-body Brenner potential with those of ab-initio studies for known reconstructions of diamond (100) and (111) surfaces. These results suggest high…

In this paper we present a few properties of $K$-partitions, which are partitions of Baire spaces such that all subfamilies of such a partition sum to a set with the Baire property. Among the result proven we have general existence result…

We prove a conjecture by W. Bergweiler and A. Eremenko on the traces of elements of modular group in this paper

In their study of a binomial sum related to Wolstenholme's theorem, Chamberland and Dilcher prove that the corresponding sequence modulo primes $p$ satisfies congruences that are analogous to Lucas' theorem for the binomial coefficients…

Plane partition diamonds were introduced by Andrews, Paule, and Riese (2001) as part of their study of MacMahon's $\Omega$-operator in search for integer partition identities. More recently, Dockery, Jameson, Sellers, and Wilson (2024)…

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

We show that the abc Conjecture implies the Weak Diversity Conjecture of Bilu and Luca.

The twisted partition monoid $\mathcal{P}_n^\Phi$ is an infinite monoid obtained from the classical finite partition monoid $\mathcal{P}_n$ by taking into account the number of floating components when multiplying partitions. The main…

In this article, we prove under some hypothesis of non ramification, a conjecture of Kottwitz and Rapoport giving the existence of crystals with additional structures.