相关论文: On equidistribution theorem for plane partitions

This paper shows that the number of hooks of length k contained in all partitions of n equals k times the number of parts of length k in all partitions of n. It contains also formulas for the moments (under uniform distribution) of k-th…

We present a study of three families of Kronecker coefficients, which we describe in terms of reduced Kronecker coefficients. This study is grounded on the generating function of the coefficients, proved by a bijection between two…

This study investigates the connection between boxed UC plane partitions and the two-site generalized phase model. By introducing two maps, we investigate the representation of two-side generalized phase algebras and actions of monodromy…

We prove several results of the following type: any $d$ measures in $\mathbb R^d$ can be partitioned simultaneously into $k$ equal parts by a convex partition (this particular result is proved independently by Pablo Sober\'on). Another…

Recently, Griffin, Ono, and Tsai examined the distribution of the number of $t$-hooks in partitions of $n$, which was later followed by the work of Craig, Ono, and Singh on the distribution of the number of $t$-hooks in self-conjugate…

The number of plane partitions contained in a given box was shown by MacMahon to be given by a simple product formula. By a simple bijection, this formula also enumerates lozenge tilings of hexagons of side-lengths $a,b,c,a,b,c$ (in cyclic…

In the theory of configuration spaces, "splitting" usually refers to the phenomenon that the configuration spaces on a manifold and those on its punctured version are closely related cohomologically. We prove a splitting theorem that is…

We establish some bounds on the number of higher-dimensional partitions by volume. In particular, we give bounds via vector partitions and MacMahon's numbers.

MacMahon's classical theorem on the number of boxed plane partitions has been generalized in several directions. One way to generalize the theorem is to view boxed plane partitions as lozenge tilings of a hexagonal region and then…

The plane partition polynomial $Q_n(x)$ is the polynomial of degree $n$ whose coefficients count the number of plane partitions of $n$ indexed by their trace. Extending classical work of E.M. Wright, we develop the asymptotics of these…

In this paper, we introduce a natural geometric extension of the partition function. More precisely, we investigate the problem of counting partitions of a rectangle into rectangular blocks with integer sides. Here, two partitions of a…

For convex partitions of a convex body $B$ we prove that we can put a homothetic copy of $B$ into each set of the partition so that the sum of homothety coefficients is $\ge 1$. In the plane the partition may be arbitrary, while in higher…

We use an injection method to prove a new class of partition inequalities involving certain $q$-products with two to four finitization parameters. Our new theorems are a substantial generalization of work by Andrews and of previous work by…

We show that the notion of mutual statistics arises naturally from the representation theory of the braid group over the multi-sheeted surface. A Hamiltonian which describes particles moving on the double-sheeted surface is proposed as a…

In the paper, the quantum-statistical approach is used to estimate the number of restricted plane partitions of an integer $n$ with the number of parts not exceeding some finite $N$. The analogy between this number-theoretical problem and…

Inequalities are important features in the context of sequences of numbers and polynomials. The Bessenrodt--Ono inequality for partition numbers and Nekrasov--Okounkov polynomials has only recently been discovered. In this paper we study…

This article presents uniform random generators of plane partitions according to the size (the number of cubes in the 3D interpretation). Combining a bijection of Pak with the method of Boltzmann sampling, we obtain random samplers that are…

We prove existence of equal area partitions of the unit sphere via optimal transport methods, accompanied by diameter bounds written in terms of Monge--Kantorovich distances. This can be used to obtain bounds on the expectation of the…

This paper, about a fluid-like system of spatially confined particles, reveals the analytic structure for both, the canonical and grand canonical partition functions. The studied system is inhomogeneously distributed in a region whose…

\noindent The simultaneous partition problems are classical problems of the combinatorial geometry which have the natural flavor of the equivariant topology. The $k$-fan partition problems have attracted a lot of attention \cite{Aki2000},…