Related papers: Reciprocity between partitions and compositions
The aim of this paper is to develop the combinatorics of constructions associated to what we call \emph{triangular partitions}. As introduced in arXiv:2102.07931, these are the partitions whose cells are those lying below the line joining…
We define noncrossing partitions of a marked surface without punctures (interior marked points). We show that the natural partial order on noncrossing partitions is a graded lattice and describe its rank function topologically. Lower…
We give a combinatorial proof of a result in rank 2 Donaldson-Thomas theory, which states that the generating function for certain plane-partition-like objects, called double-box configurations, is equal to a product of MacMahon's…
In this article we prove several reciprocity theorems for some infinite-dimensional dual pairs of representations on Bargmann-Segal-Fock spaces.
We study the correlations (and alignment as a particular case) existent between the fragments originated in a decaying process when the daughter particles interact. The interaction between the particles is modeled using the potential of…
We construct an easily described family of partitions of the positive integers into $n$ disjoint sets with essentially the same structure for every $n \geq 2$. In a special case, it interpolates between the Beatty $\frac{1}{\phi} +…
It is proved that every linear biseparating map between spaces of vector-valued differentiable functions is a weighted composition map. As a consequence, such a map is always continuous.
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…
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…
In recent work, G. E. Andrews and G. Simay prove a surprising relation involving parity palindromic compositions, and ask whether a combinatorial proof can be found. We extend their results to a more general class of compositions that are…
Motivated by examples of symmetrically constrained compositions, super convex partitions, and super convex compositions, we initiate the study of partitions and compositions constrained by graph Laplacian minors. We provide a complete…
We study the structure of two cointeracting bialgebras on noncrossing partitions appearing in the theory of free probability. The first coproduct is given by separation of the blocks of the partitions into two parts, with respect to the…
We construct an involution on set partitions which keeps track of the numbers of crossings, nestings and alignments of two edges. We derive then the symmetric distribution of the numbers of crossings and nestings in partitions, which…
Andrews and El Bachraoui recently studied integer partitions where the smallest part is repeated a specified number of times and any other parts are distinct. Their results included two ``surprising identities'' for which they requested…
A construction is given of Markov partitions for some rational maps, which persist over regions of parameter space, not confined to single hyperbolic components. The set on which the Markov partition exists, and its boundary, are analysed.
We consider Kingman's partition structures which are regenerative with respect to a general operation of random deletion of some part. Prototypes of this class are the Ewens partition structures which Kingman characterised by regeneration…
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…
It is known that partial spreads is a class of bent partitions. In \cite{AM2022Be,MP2021Be}, two classes of bent partitions whose forms are similar to partial spreads were presented. In \cite{AKM2022Ge}, more bent partitions $\Gamma_{1},…
A new algorithm for inserting rim-hooks into reverse plane partitions is presented. The insertion is used to define a bijection between reverse plane partitions of a fixed shape and multi-sets of rim-hooks. In turn this yields a bijective…
In this paper, we study bounded and closed range multiplication and composition operators between two different Orlicz spaces.