Related papers: Hook-lengths and Pairs of Compositions
A relational structure is homomorphism-homogeneous if every homomorphism between finite substructures extends to an endomorphism of the structure. This notion was introduced recently by Cameron and Ne\v{s}et\v{r}il. In this paper we…
In this paper we introduce and investigate a one-parameter family of polynomials. They are semisymmetric, i.e. symmetric in the variables with odd and even index separately. In fact, the family forms a basis of the space of semisymmetric…
It is known that the number of minimal factorizations of the long cycle in the symmetric group into a product of $k$ cycles of given lengths has a very simple formula: it is $n^{k-1}$ where $n$ is the rank of the underlying symmetric group…
In this paper, we study algorithmic questions concerning products of matrices and their consequences for recognition algorithms for polyhedra. The 1-product of matrices $S_1$, $S_2$ is a matrix whose columns are the concatenation of each…
A vector species is a functor from the category of finite sets with bijections to vector spaces (over a fixed field); informally, one can view this as a sequence of $S_n$-modules. A Hopf monoid (in the category of vector species) consists…
Lock polynomials and lock Kohnert tableaux are natural analogues to key polynomials and key Kohnert tableaux, respectively. In this paper, we compare lock polynomials to the much-studied key polynomials and show that the difference of a key…
A Hadamard-Hitchcock decomposition of a multidimensional array is a decomposition that expresses the latter as a Hadamard product of several tensor rank decompositions. Such decompositions can encode probability distributions that arise…
In many classification tasks there is a requirement of monotonicity. Concretely, if all else remains constant, increasing (resp. decreasing) the value of one or more features must not decrease (resp. increase) the value of the prediction.…
We explore a natural extension of braid arrangements in the context of determinantal arrangements. We show that these determinantal arrangements are free divisors. Additionally, we prove that free determinantal arrangements defined by the…
The M-polynomial provides a unifying framework for a wide class of degree-based topological indices. Despite its structural importance, general methods for computing the M-polynomial under graph constructions remain limited. In this paper,…
We present a framework for the construction of linearizations for scalar and matrix polynomials based on dual bases which, in the case of orthogonal polynomials, can be described by the associated recurrence relations. The framework…
We introduce a notion of substitutability for correspondences and establish a monotone comparative static result, unifying results such as the inverse isotonicity of M-matrices, Berry, Gandhi and Haile's identification of demand systems,…
In current applied research the most-used route to an analysis of composition is through log-ratios -- that is, contrasts among log-transformed measurements. Here we argue instead for a more direct approach, using a statistical model for…
We consider polynomial maps of the form f(z,w) = (p(z),q(z,w)) that extend as holomorphic maps of CP^2. Mattias Jonsson introduces in (Math. Ann., 1999) a notion of connectedness for such polynomial skew products that is analogous to…
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…
Several hook summation formulae for binary trees have appeared recently in the literature. In this paper we present an analogous formula for unordered increasing trees of size r, which involves r parameters. The right-hand side can be…
We consider a class of pattern matching problems where a normalising transformation is applied at every alignment. Normalised pattern matching plays a key role in fields as diverse as image processing and musical information processing…
We study the monodromy groups of compositions of two indecomposable polynomials. In particular, we show that such monodromy groups either fulfill a certain "largeness" property, or are in an explicit list of exceptions. Such largeness…
In combinatorics, a derangement is a permutation that has no fixed points. The number of derangements of an n-element set is called the n-th derangement number. In this paper, as natural companions to derangement numbers and degenerate…
We discuss inequalities between the values of \emph{homotopical and cohomological Poincar\'e polynomials} of the self-products of rationally elliptic spaces. For rationally elliptic quasi-projective varieties, we prove inequalities between…