相关论文: Self-complementary plane partitions by Proctor's m…

We obtain a new family of relations satisfied by the partition function. In contrast with most partition relations, these involve non-trivial roots of unity. We present two proofs, one using the fact that the discriminant modular form is a…

We prove the existence of complexified real arrangements with the same combinatorics but different embeddings in the complex projective plane. Such pair of arrangements has an additional property: they admit conjugated equations on the ring…

Using a calculus of variations approach, we determine the shape of a typical plane partition in a large box (i.e., a plane partition chosen at random according to the uniform distribution on all plane partitions whose solid Young diagrams…

We provide a new foundation for combinatorial commutative algebra and Stanley-Reisner theory using the partition complex introduced in [Adi18]. One of the main advantages is that it is entirely self-contained, using only a minimal knowledge…

Given a minuscule representation of a simple Lie algebra, we find an algebraic model for the action of a regular element and show that these models can be glued together over the adjoint quotient, viewed as the set of all regular conjugacy…

Applications of harmonic analysis on finite groups were recently introduced to measure partition problems, with a variety of equipartition types by convex fundamental domains obtained as the vanishing of prescribed Fourier transforms.…

We give a new method for manufacturing complete minimal submanifolds of compact Lie groups and their homogeneous quotient spaces. For this we make use of harmonic morphisms and basic representation theory of Lie groups. We then apply our…

We study the combinatorics of pseudoline arrangements in the real projective plane. Our focus lies on two classes of arrangements: simplicial arrangements and arrangements whose characteristic polynomials have only real roots. We derive…

In this article, we define and study a geometry and an order on the set of partitions of an even number of objects. One of the definitions involves the partition algebra, a structure of algebra on the set of such partitions depending on an…

We construct the ordinary irreducible representations of the group of automorphisms of a finite rooted tree and we get a natural parametrization of them. To achieve this goals, we introduce and study the combinatorics of tree compositions,…

The exactly solvable four-vertex model with the fixed boundary conditions in the presence of inhomogeneous linearly growing external field is considered. The partition function of the model is calculated and represented in the determinantal…

Hyperplane arrangements form the latest addition to the zoo of combinatorial objects dealt with by polymake. We report on their implementation and on a algorithm to compute the associated cell decomposition. The implemented algorithm…

We present a simple bijection between permutation matrices and descending plane partitions without special parts. This bijection is already mentioned in work of P. Lalonde (without giving the details); it involves the inversion words of…

A triangular partition is a partition whose Ferrers diagram can be separated from its complement (as a subset of $\mathbb{N}^2$) by a straight line. Having their origins in combinatorial number theory and computer vision, triangular…

We study the combinatorics of hyperplane arrangements over arbitrary fields. Specifically, we determine in which situation an arrangement and its reduction modulo a prime number have isomorphic lattices via the use of minimal strong…

The group algebra of the permutation group is spanned by a set of elements called projectors. The coordinates of permutations expanded in projectors are matrix elements of irreducible representations. The projectors of the permutation group…

We prove identities generating higher dimensional vector partitions. We derive theorems for integer lattice points in the 2D first quadrant, then generalize the approach to find 3D and $n$-space lattice point vector region extensions. We…

Mass partition problems describe the partitions we can induce on a family of measures or finite sets of points in Euclidean spaces by dividing the ambient space into pieces. In this survey we describe recent progress in the area in addition…

In this paper, we use a simple discrete dynamical model to study integer partitions and their lattice. The set of reachable configurations of the model, with the order induced by the transition rule defined on it, is the lattice of all…

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…