MATHEMATICA SCANDINAVICA https://www.mscand.dk/ Mathematica Scandinavica en-US MATHEMATICA SCANDINAVICA 0025-5521 Subalgebras generated in degree two with minimal Hilbert function https://www.mscand.dk/article/view/122603 <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.&nbsp;Boij and A.&nbsp;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> Lisa Nicklasson Copyright (c) 2021 MATHEMATICA SCANDINAVICA 2021-02-17 2021-02-17 127 1 5 27 10.7146/math.scand.a-122603 Pro-$p$ groups with few relations and universal Koszulity https://www.mscand.dk/article/view/123644 <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.&nbsp;Miná{č} et al. in the case of maximal pro-$p$ Galois groups of fields with at most $2$ defining relations.</p> Claudio Quadrelli Copyright (c) 2021 MATHEMATICA SCANDINAVICA 2021-02-17 2021-02-17 127 1 28 42 10.7146/math.scand.a-123644 Hypergroups and distance distributions of random walks on graphs https://www.mscand.dk/article/view/122932 <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> Kenta Endo Ippei Mimura Yusuke Sawada Copyright (c) 2021 MATHEMATICA SCANDINAVICA 2021-02-17 2021-02-17 127 1 43 62 10.7146/math.scand.a-122932 On the structure of open equivariant topological conformal field theories https://www.mscand.dk/article/view/122371 <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> Ramsès Fernàndez-València Copyright (c) 2021 MATHEMATICA SCANDINAVICA 2021-02-17 2021-02-17 127 1 63 78 10.7146/math.scand.a-122371 Rational quartic spectrahedra https://www.mscand.dk/article/view/121456 <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> Martin Helsø Kristian Ranestad Copyright (c) 2020 MATHEMATICA SCANDINAVICA 2021-02-17 2021-02-17 127 1 79 99 10.7146/math.scand.a-121456 Randers Ricci soliton homogeneous nilmanifolds https://www.mscand.dk/article/view/122610 <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> Hamid Reza Salimi Moghaddam Copyright (c) 2021 MATHEMATICA SCANDINAVICA 2021-02-17 2021-02-17 127 1 100 110 10.7146/math.scand.a-122610 Logarithmic concavity of the inverse incomplete beta function with respect to the first parameter https://www.mscand.dk/article/view/121924 <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> Dimitris Askitis Copyright (c) 2021 MATHEMATICA SCANDINAVICA 2021-02-17 2021-02-17 127 1 111 130 10.7146/math.scand.a-121924 A revised augmented Cuntz semigroup https://www.mscand.dk/article/view/121016 <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> Leonel Robert Luis Santiago Copyright (c) 2021 MATHEMATICA SCANDINAVICA 2021-02-17 2021-02-17 127 1 131 160 10.7146/math.scand.a-121016 Issue covers https://www.mscand.dk/article/view/125053 <p>Issue covers</p> Mathematica Scandinavica Copyright (c) 0 2021-02-17 2021-02-17 127 1 Volume title pages https://www.mscand.dk/article/view/125054 <p>Volume title pages</p> Mathematica Scandinavica Copyright (c) 2021 MATHEMATICA SCANDINAVICA 2021-02-17 2021-02-17 127 1 1 4 10.7146/math.scand.a-125054