Related papers: More Heffter Spaces via finite fields

A {\it vector space partition} is here a collection $\mathcal P$ of subspaces of a finite vector space $V(n,q)$, of dimension $n$ over a finite field with $q$ elements, with the property that every non zero vector is contained in a unique…

The rank of a hierarchically hyperbolic space is the maximal number of unbounded factors in a standard product region. For hierarchically hyperbolic groups, this coincides with the maximal dimension of a quasiflat. Examples for which the…

Hilbert spaces in theories of gravity are notoriously subtle due to the Hamiltonian constraints, particularly regarding the inner product. To demystify this subject, we review and extend a collection of ideas in canonical gravity, and…

We say that a linear space is harmonious if it is resolvable and admits an automorphism group acting sharply transitively on the points and transitively on the parallel classes. Generalizing old results by the first author et al. we present…

A coregular space is a representation of an algebraic group for which the ring of polynomial invariants is free. In this paper, we show that the orbits of many coregular irreducible representations where the number of invariants is at least…

An orthogonality space is a set equipped with a symmetric and irreflexive binary relation. We consider orthogonality spaces with the additional property that any collection of mutually orthogonal elements gives rise to the structure of a…

We prove that if a subset of a $d$-dimensional vector space over a finite field with $q$ elements has more than $q^{d-1}$ elements, then it determines all the possible directions. If a set has more than $q^k$ elements, it determines a…

We prove an extension of the homology version of the Hofer-Zehnder conjecture proved by Shelukhin to the weighted projective spaces which are symplectic orbifolds. In particular, we prove that if the number of fixed points counted with…

Let $P \subset \mathbb{R}^{d}$ be a closed convex cone. Assume that $P$ is pointed, i.e. the intersection $P \cap -P=\{0\}$ and $P$ is spanning, i.e. $P-P=\mathbb{R}^{d}$. Denote the interior of $P$ by $\Omega$. Let $E$ be a product system…

In a k-linear triangulated category (where k is a field) we show that the existence of Auslander-Reiten triangles implies that objects are determined, up to shift, by knowing dimensions of homomorphisms between them. In most cases the…

Let $G=QD_{8k}~$ be the quasi-dihedral group of order $8n$ and $\theta$ be an automorphism of $QD_{8k}$ of finite order. The fixed-point set $H$ of $\theta$ is defined as $H_{\theta}=G^{\theta}=\{x\in G \mid \theta(x)=x\}$ and generalized…

Archdeacon, in his seminal paper $[1]$, defined the concept of Heffter array to provide explicit constructions of biembeddings of the complete graph $K_v$ into orientable surfaces, the so-called Archdeacon embeddings, and proved that these…

Motivated by the theory of locally definable groups, we study the theory of $K$-vector spaces with a predicate for the union $X$ of an infinite family of independent subspaces. We show that if $K$ is infinite then the theory is complete and…

We construct the hyper-K\"ahler moduli space of framed monopoles over $\mathbb{R}^3$ for any connected, simply connected, compact, semisimple Lie group and arbitrary mass and charge, and hence symmetry breaking. In order to do so, we define…

We explain why and how the Hilbert space comes about in quantum theory. The axiomatic structures of vector space, of scalar product, of orthogonality, and of the linear functional are derivable from the statistical description of quantum…

It is shown in the paper that each Hecke symmetry R with the R-symmetric algebra freely generated by 3 commuting elements is determined by a bivector and a symmetric bilinear form on a 3-dimensional vector space. A general formula for such…

Let $K$ be a global field or $\overline{\mathbb Q}$, $F$ a nonzero quadratic form on $K^N$, $N \geq 2$, and $V$ a subspace of $K^N$. We prove the existence of an infinite collection of finite families of small-height maximal totally…

The purpose of the paper is to introduce and study a new class of operators on semi-Hilbertian spaces i.e.; spaces generated by positive semidefinite sesquilinear forms. Let H be a Hilbert space and let A be a positive bounded operator on H…

A ringed finite space is a ringed space whose underlying topological space is finite. The category of ringed finite spaces contains, fully faithfully, the category of finite topological spaces and the category of affine schemes. Any ringed…

We develop a theory of ordered *-vector spaces with an order unit. We prove fundamental results concerning positive linear functionals and states, and we show that the order (semi)norm on the space of self-adjoint elements admits multiple…