Related papers: Equivariant lattice generators and Markov bases
We show that for any finitely generated group of matrices that is not virtually solvable, there is an integer m such that, given an arbitrary finite generating set for the group, one may find two elements a and b that are both products of…
In this article an explicit method (relying on representation theory) to construct packings in Grassmannian space is presented. Infinite families of configurations having only one non-trivial set of principal angles are found using…
In many applications involving binary variables, only pairwise dependence measures, such as correlations, are available. However, for multi-way tables involving more than two variables, these quantities do not uniquely determine the joint…
Algorithmic computation in polynomial rings is a classical topic in mathematics. However, little attention has been given to the case of rings with an infinite number of variables until recently when theoretical efforts have made possible…
We prove that a monomial ideal $I$ generated in a single degree, is polymatroidal if and only if it has linear quotients with respect to the lexicographical ordering of the minimal generators induced by every ordering of variables. We also…
Two parameter families of plane conics are called nets of conics. There is a natural group action on the vector space of nets of conics, namely the product of the group reparametrizing the underlying plane, and the group reparametrizing the…
We characterize the infinitesimal generator of a semigroup of linear fractional self-maps of the unit ball in $\mathbb C^n$, $n\geq 1$. For the case $n=1$ we also completely describe the associated Koenigs function and we solve the…
Two finite words $u$ and $v$ are $k$-binomially equivalent if, for each word $x$ of length at most $k$, $x$ appears the same number of times as a subsequence (i.e., as a scattered subword) of both $u$ and $v$. This notion generalizes…
In any connected non-compact semi-simple Lie group without factors locally isomorphic to SL_2(R), there can be only finitely many lattices (up to isomorphism) of a given covolume. We show that there exist arbitrarily large families of…
We present a new approach to construct $T$-equivariant flat toric degenerations of flag varieties and spherical varieties, combining ideas coming from the theory of Newton-Okounkov bodies with ideas originally stemming from PBW-filtrations.…
We give a uniform explicit construction of finite two-generator presentations for the special linear groups over the integers in all ranks at least three. The construction builds on the generating-pair work of Conder--Liversidge--Vsemirnov…
Recently George Bergman proved that the symmetric group of an infinite set possesses the following property which we call by the {\it universality of finite width}: given any generating set $X$ of the symmetric group of an infinite set…
We study linear systems cut out by cones of fixed degree on a smooth complex curve $C\subset\mathbb{P}^{3}$. We develop a systematic study of the families of such systems, considering their limits, their infinitesimal behaviour and some…
The paper describes the algebraic structure of the graded algebra of differentially homogeneous polynomials of fixed finite order. We show that it is a finitely generated algebra, and we exhibit a minimal set of generators. Along the way,…
We use difference sets to construct interesting sets of lines in complex space. Using (v,k,1)-difference sets, we obtain k^2-k+1 equiangular lines in C^k when k-1 is a prime power. Using semiregular relative difference sets with parameters…
The classical matrix tree theorem relates the number of spanning trees of a connected graph with the product of the nonzero eigenvalues of its Laplacian matrix. The class of regular matroids generalizes that of graphical matroids, and a…
Recently, some infinite families of binary minimal and optimal linear codes are constructed from simplicial complexes by Hyun {\em et al}. Inspired by their work, we present two new constructions of codes over the ring $\Bbb F_2+u\Bbb F_2$…
This paper shows that orbital equations generated by iteration of polynomial maps do not have necessarily a unique representation. Remarkably, they may be represented in an infinity of ways, all interconnected by certain nonlinear…
In a recent paper Cameron, Lakshmanan and Ajith began an exploration of hypergraphs defined on algebraic structures, especially groups, to investigate whether this can add a new perspective. Following their suggestions, we consider suitable…
We study certain lattices constructed from finite abelian groups. We show that such a lattice is eutactic, thereby confirming a conjecture by B\"ottcher, Eisenbarth, Fukshansky, Garcia, Maharaj. Our methods also yield simpler proofs of two…