Related papers: The skew-growth function on the monoid of square m…

Let $M$ be a positive homogeneously presented cancellative monoid ${< L \mid R >}_{mo}$ equipped with the degree map $\deg:M \to \Z_{\ge0}$ defined by assigning to each equivalence class of words the length of the words, and let $P_{M,…

If a finitely generated monoid M is defined by a finite number of degree-preserving relations, then it has linear growth if and only if it can be decomposed into a finite disjoint union of subsets (which we call "sandwiches") of the form…

We compute the dimensions of $\text{GL}_N$-skein modules of genus-one mapping tori $T^2\times_\gamma S^1$, for an arbitrary diffeomorphism of $T^2$, and for generic quantum parameter. These are most cleanly expressed via a generating…

The skew monoidal categories of Szlach\'anyi are a weakening of monoidal categories where the three structural laws of left and right unitality and associativity are not required to be isomorphisms but merely transformations in a particular…

Skew-representable matroids form a fundamental class in matroid theory, bridging combinatorics and linear algebra. They play an important role in areas such as coding theory, optimization, and combinatorial geometry, where linear structure…

Let $G_{M}^{+}$ be the Artin monoid of finite type generated by the letters $a_i, i\in I$ with respect to a Coxeter matrix $M$ that is equipped with the degree map $\deg\!:\!G_{M}^{+} \to\!\Z_{\ge0}$ defined by assigning to each equivalence…

In this work, linearized multivariate skew polynomials over division rings are introduced. Such polynomials are right linear over the corresponding centralizer and generalize linearized polynomial rings over finite fields, group rings or…

Skew-monoidal categories arise when the associator and the left and right units of a monoidal category are, in a specific way, not invertible. We prove that the closed skew-monoidal structures on the category of right R-modules are…

We show that the skew-growth function of a dual Artin monoid of finite type P has exactly rank(P) =: l simple real zeros on the interval (0, 1]. The proofs for types A_l and B_l are based on an unexpected fact that the skew-growth…

We consider a natural generalization of braids which we call shrinking braids. We state the relations of shrinking braids and use them to define algebraically the monoid $R$. We endow a subset of $R$ with a \emph{left distributive monoid}…

For a semigroup $S$ whose universal right congruence is finitely generated (or, equivalently, a semigroup satisfying the homological finiteness property of being type right-$FP_1$), the right diameter of $S$ is a parameter that expresses…

Let $M$ be a finitely generated skew field over a ground field $k$, and let $G$ be a finite group of $k$-linear automorphisms of $M$. This paper investigates finite generation of the skew subfield $M^G$ of $G$-invariants in $M$, and…

Starting from a master equation, we derive the evolution equation for the size distribution of elements in an evolving system, where each element can grow, divide into two, and produce new elements. We then probe general solutions of the…

Monoidal closed categories naturally model NMILL, non-commutative multiplicative intuitionistic linear logic: the monoidal unit and tensor interpret the multiplicative verum and conjunction; the internal hom interprets linear implication.…

It is known to be difficult to find out whether a certain multivariable function to be a characteristic function when its corresponding measure is not tirivial to be or not to be a probability measure on R^d. Such results were not obtained…

We consider the problem of random uniform generation of traces (the elements of a free partially commutative monoid) in light of the uniform measure on the boundary at infinity of the associated monoid. We obtain a product decomposition of…

We show that a specialization in Weyl character formula can be carried out in such a way that its right-hand side becomes simply a Schur Function. For this, we need the use of fundamental weights. In the generic definition, an Elementary…

We show the following version of the Schur's product theorem. If $M=(M_{j,k})_{j,k=1}^n\in{\mathbb R}^{n\times n}$ is a positive semidefinite matrix with all entries on the diagonal equal to one, then the matrix $N=(N_{j,k})_{j,k=1}^n$ with…

Given two m x n matrices A = (a_{ij}) and B=(b_{ij}) with entries in B(H), the Schur block product is the m x n matrix A \square B := (a_{ij}b_{ij}). There exists an m x n contraction matrix S = (s_{ij}), such that A \square B =…

We establish recurrences formulas of the order of the classical groups that allow us to find a generalization of Euler's angles for classical groups and the invariant measures of these groups. We find the generating function for the SU(2)…