Related papers: A bijection between strongly stable and totally sy…
Topologically stable cellular partitions of D dimensional spaces are studied. A complete statistical description of the average structural properties of such partition is given in term of a sequence of D/2-1 (or (D-1)/2) variables for D…
Aim of this paper is to count $0$-dimensional stable and strongly stable ideals in $2$ and $3$ variables, given their (constant) affine Hilbert polynomial. To do so, we define the Bar Code, a bidimensional structure representing any finite…
We study some combinatorial properties of higher-dimensional partitions which generalize plane partitions. We present a natural bijection between $d$-dimensional partitions and $d$-dimensional arrays of nonnegative integers. This bijection…
We study two partial orders on $[x_1,...,x_n]$, the free abelian monoid on ${x_1,...,x_n}$. These partial orders, which we call the ``strongly stable'' and the ``stable'' partial order, are defined by the property that their filters are…
We give a construction for the d-dimensional simplices with all distances in {1,2} from the set of partitions of d+1.
In this paper we present a new class of integer partition identities. The number of partitions with d-distant parts can be represented as a sum of the number of partitions with 1-distant parts whose even parts are greater than twice the…
This paper introduces the concept of dimensional stability for spline spaces over T-meshes, providing the first mathematical definition and a preliminary classification framework. We define dimensional stability as an invariant within the…
Strongly stable monomial ideals are important in algebraic geometry, commutative algebra, and combinatorics. Prompted, for example, by combinatorial approaches for studying Hilbert schemes and the existence of maximal total Betti numbers…
Let $\mathcal{H}_d^{(t)}$ ($t \geq -d$, $t>-3$) be the reproducing kernel Hilbert space on the unit ball $\mathbb{B}_d$ with kernel \[ k(z,w) = \frac{1}{(1-\langle z, w \rangle)^{d+t+1}} . \] We prove that if an ideal $I \triangleleft…
We characterize separable multidimensional permutations in terms of forbidden patterns and enumerate them by means of generating function, recursive formula and explicit formula. We find a connection between multidimensional permutations…
Recently, Schneider and Schneider defined a new class of partitions called sequentially congruent partitions, in which each part is congruent to the next part modulo its index, and they proved two partition bijections involving these…
A geometrical characterization of robustly separable (that is, remaining separable under sufficiently small variiations) mixed states of a bipartite quantum system is given. It is shown that the density matrix of any such state can be…
We investigate the Euclidean $d$-Dimensional Stable Roommates problem, which asks whether a given set~$V$ of $d \cdot n$ points from the 2-dimensional Euclidean space can be partitioned into $n$ disjoint (unordered) subsets…
Alternative novel measures of the distance between any two partitions of a n-set are proposed and compared, together with a main existing one, namely 'partition-distance' D(.,.). The comparison achieves by checking their restriction to…
In this note a bijection is constructed between the set of partitions of n simultaneously s-regular and t-distinct, and those simultaneously t-regular and s-distinct. Some implications of the map are discussed. As a generalized version of…
In the Stable Roommates problem, we seek a stable matching of the agents into pairs, in which no two agents have an incentive to deviate from their assignment. It is well known that a stable matching is unlikely to exist, but a stable…
We prove that the space of complex irreducible polynomials of degree $d$ in $n$ variables satisfies two forms of homological stability: first, its cohomology stabilizes as $d$ increases, and second, its compactly supported cohomology…
The purpose of this paper is to initiate a new attack on Arveson's resistant conjecture, that all graded submodules of the $d$-shift Hilbert module $H^2$ are essentially normal. We introduce the stable division property for modules (and…
Two-dimensional (2D) fundamental soliton-soliton pairs are investigated in binary mixtures of Bose-Einstein condensates with attractive interactions between atoms of the same type. Both attractive and repulsive interactions between atoms of…
We enrich the setting of strongly stable ideals (SSI): We introduce shift modules, a module category encompassing SSI's. The recently introduced duality on SSI's is given an effective conceptual and computational setting. We study strongly…