https://www.mscand.dk/issue/feedMATHEMATICA SCANDINAVICA2021-04-21T03:41:26+02:00Arne Jensenmscand@math.au.dkOpen Journal Systemshttps://www.mscand.dk/article/view/122603Subalgebras generated in degree two with minimal Hilbert function2021-04-21T03:41:01+02:00Lisa Nicklassonmscand@math.au.dk<p>What can be said about the subalgebras of the polynomial ring, with minimal or maximal Hilbert function? This question was discussed in a recent paper by M. Boij and A. Conca. In this paper we study the subalgebras generated in degree two with minimal Hilbert function. The problem to determine the generators of these algebras transfers into a combinatorial problem on counting maximal north-east lattice paths inside a shifted Ferrers diagram. We conjecture that the subalgebras generated in degree two with minimal Hilbert function are generated by an initial Lex or RevLex segment.</p>2021-02-17T00:00:00+01:00Copyright (c) 2021 MATHEMATICA SCANDINAVICAhttps://www.mscand.dk/article/view/123644Pro-$p$ groups with few relations and universal Koszulity2021-04-21T03:40:44+02:00Claudio Quadrellimscand@math.au.dk<p>Let $p$ be a prime. We show that if a pro-$p$ group with at most $2$ defining relations has quadratic $\mathbb{F}_p$-cohomology algebra, then this algebra is universally Koszul. This proves the “Universal Koszulity Conjecture” formulated by J. Miná{č} et al. in the case of maximal pro-$p$ Galois groups of fields with at most $2$ defining relations.</p>2021-02-17T00:00:00+01:00Copyright (c) 2021 MATHEMATICA SCANDINAVICAhttps://www.mscand.dk/article/view/122932Hypergroups and distance distributions of random walks on graphs2021-04-21T03:40:50+02:00Kenta Endomscand@math.au.dkIppei Mimuramscand@math.au.dkYusuke Sawadamscand@math.au.dk<p>Wildberger's construction enables us to obtain a hypergroup from a random walk on a special graph. We will give a probability theoretic interpretation to products on the hypergroup. The hypergroup can be identified with a commutative algebra whose basis is transition matrices. We will estimate the operator norm of such a transition matrix and clarify a relationship between their matrix products and random walks.</p>2021-02-17T00:00:00+01:00Copyright (c) 2021 MATHEMATICA SCANDINAVICAhttps://www.mscand.dk/article/view/122371On the structure of open equivariant topological conformal field theories2021-04-21T03:41:06+02:00Ramsès Fernàndez-Valènciamscand@math.au.dk<p>A classification of open equivariant topological conformal field theories in terms of Calabi-Yau $A_\infty $-categories endowed with a group action is presented.</p>2021-02-17T00:00:00+01:00Copyright (c) 2021 MATHEMATICA SCANDINAVICAhttps://www.mscand.dk/article/view/121456Rational quartic spectrahedra2021-04-21T03:41:18+02:00Martin Helsømscand@math.au.dkKristian Ranestadmscand@math.au.dk<p>Rational quartic spectrahedra in $3$-space are semialgebraic convex subsets in $\mathbb{R} ^3$ of semidefinite, real symmetric $(4 \times 4)$-matrices, whose boundary admits a rational parameterization. The Zariski closure in $\mathbb{C}\mathbb{P} ^3$ of the boundary of a rational spectrahedron is a rational complex symmetroid. We give necessary conditions on the configurations of singularities of the corresponding real symmetroids in $\mathbb{R} \mathbb{P} ^3$ of rational quartic spectrahedra. We provide an almost exhaustive list of examples realizing the configurations, and conjecture that the missing example does not occur.</p>2021-02-17T00:00:00+01:00Copyright (c) 2020 MATHEMATICA SCANDINAVICAhttps://www.mscand.dk/article/view/122610Randers Ricci soliton homogeneous nilmanifolds2021-04-21T03:40:55+02:00Hamid Reza Salimi Moghaddammscand@math.au.dk<p>Let $F$ be a left-invariant Randers metric on a simply connected nilpotent Lie group $N$, induced by a left-invariant Riemannian metric $\hat{\boldsymbol{a}}$ and a vector field $X$ which is $I_{\hat{\boldsymbol{a}}}(M)$-invariant. We show that if the Ricci flow equation has a unique solution then, $(N,F)$ is a Ricci soliton if and only if $(N,F)$ is a semialgebraic Ricci soliton.</p>2021-02-17T00:00:00+01:00Copyright (c) 2021 MATHEMATICA SCANDINAVICAhttps://www.mscand.dk/article/view/121924Logarithmic concavity of the inverse incomplete beta function with respect to the first parameter2021-04-21T03:41:12+02:00Dimitris Askitismscand@math.au.dk<p>The beta distribution is a two-parameter family of probability distributions whose distribution function is the (regularised) incomplete beta function. In this paper, the inverse incomplete beta function is studied analytically as a univariate function of the first parameter. Monotonicity, limit results and convexity properties are provided. In particular, logarithmic concavity of the inverse incomplete beta function is established. In addition, we provide monotonicity results on inverses of a larger class of parametrised distributions that may be of independent interest.</p>2021-02-17T00:00:00+01:00Copyright (c) 2021 MATHEMATICA SCANDINAVICAhttps://www.mscand.dk/article/view/121016A revised augmented Cuntz semigroup2021-04-21T03:41:26+02:00Leonel Robertmscand@math.au.dkLuis Santiagomscand@math.au.dk<p>We revise the construction of the augmented Cuntz semigroup functor used by the first author to classify inductive limits of $1$-dimensional noncommutative CW complexes. The original construction has good functorial properties when restricted to the class of C*-algebras of stable rank one. The construction proposed here has good properties for all C*-algebras: we show that the augmented Cuntz semigroup is a stable, continuous, split exact functor, from the category of C*-algebras to the category of Cu-semigroups.</p>2021-02-17T00:00:00+01:00Copyright (c) 2021 MATHEMATICA SCANDINAVICAhttps://www.mscand.dk/article/view/125053Issue covers2021-02-17T17:44:46+01:00Mathematica Scandinavicamscand@math.au.dk<p>Issue covers</p>2021-02-17T00:00:00+01:00Copyright (c) 0 https://www.mscand.dk/article/view/125054Volume title pages2021-04-21T03:40:37+02:00Mathematica Scandinavicamscand@math.au.dk<p>Volume title pages</p>2021-02-17T00:00:00+01:00Copyright (c) 2021 MATHEMATICA SCANDINAVICA