Related papers: Factorization length distribution for affine semig…
We associate a cohomological invariant to each outer action of a group on a factor, and classify them by the invariant in the case that the group is a countable discrete amenable group and the factor is appoximately finite dimensional. The…
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…
An atomic monoid $M$ is called length-factorial if for every non-invertible element $x \in M$, no two distinct factorizations of $x$ into irreducibles have the same length (i.e., number of irreducible factors, counting repetitions). The…
We generalize the notion of symmetric semigroups, pseudo symmetric semigroups, and row factorization matrices for pseudo Frobenius elements of numerical semigroups to the case of semigroups with maximal projective dimension (MPD…
Factorization properties of one-loop gauge theory amplitudes have been used as checks on explicitly computed amplitudes and in the construction of ansatze for higher-point ones. In massless theories, such as QCD at high energies, infrared…
Two semimetrics on probability distributions are proposed, given as the sum of differences of expectations of analytic functions evaluated at spatial or frequency locations (i.e, features). The features are chosen so as to maximize the…
A new class of two-level non-regular fractional factorial designs is defined. We call this class an {\it affinely full-dimensional factorial design}, meaning that design points in the design of this class are not contained in any affine…
It is shown that some convolution semigroups of infinitely divisible measures are invariant under the random integral mappings $I^{h,r}_{(a,b]}$ defined in $(\star)$ below. The converse implication is specified for the semigroups of…
The modal factor model represents a new factor model for dimension reduction in high dimensional panel data. Unlike the approximate factor model that targets for the mean factors, it captures factors that influence the conditional mode of…
A complication in proving factorization theorems in Feynman gauge is that individual graphs give a super-leading power of the hard scale when all the gluons inducing the hard scattering are longitudinally polarized. With the aid of an…
This report aims to characterise certain sojourn time distributions that naturally arise from semi-Markov models. To this end, it describes a family of discrete distributions that extend the geometric distribution for both finite and…
The asymptotic study of the conjugacy classes of a random element of the finite affine group leads one to define a probability measure on the set of all partitions of all positive integers. Four different probabilistic understandings of…
In this article we consider the cycle structure of compositions of pairs of involutions in the symmetric group S_n chosen uniformly at random. These can be modeled as modified 2-regular graphs, giving rise to exponential generating…
This article discusses numerical semigroups having a generator which is as large as possible. This turns out to be $2g+1$, where $g$ is the genus of the semigroup. We will show that these semigroups are closely related to symmetric…
In this paper we consider suitable families of power series distributed random variables, and we study their asymptotic behavior in the fashion of large (and moderate) deviations. We also present two examples of fractional counting…
Given a join semilattice $S$ with a minimum $\hat{0}$, the quarks (also called atoms in order theory) are the elements that cover $\hat{0}$, and for each $x \in S \setminus \{\hat{0}\}$ a factorization (into quarks) of $x$ is a minimal set…
This work investigates the rank properties of $A^+(B_n)$, the multiplicative semigroup reduct of the affine near-semirings over an aperiodic Brandt semigroup $B_n$. In this connection, the work obtains the small rank, lower rank and large…
A numerical semigroup is a sub-semigroup of the natural numbers that has a finite complement. The size of its complement is called the genus and the largest number in the complement is called its Frobenius number. We consider the set of…
The algebraic properties of formal power series, whose coefficients show factorial growth and admit a certain well-behaved asymptotic expansion, are discussed. It is shown that these series form a subring of $\mathbb{R}[[x]]$. This subring…
We continue our study of exponent semigroups of rational matrices. Our main result is that the matricial dimension of a numerical semigroup is at most its multiplicity (the least generator), greatly improving upon the previous upper bound…