Related papers: Potentials of a Frobenius like structure
In this paper, we characterize the (generalized) Frobenius powers and critical exponents of two classes of monomial ideals of a polynomial ring in positive characteristic: powers of the homogeneous maximal ideal, and ideals generated by…
In this paper we outline a Matrix Ansatz approach to some problems of combinatorial enumeration. The idea is that many interesting quantities can be expressed in terms of products of matrices, where the matrices obey certain relations. We…
We discuss when the incidence coalgebra of a locally finite preordered set is right co-Frobenius. As a consequence, we obtain that a structural matrix algebra over a field $k$ is Frobenius if and only if it consists, up to a permutation of…
It is known that the quantale of sup-preserving maps from a complete lattice to itself is a Frobenius quantale if and only if the lattice is completely distributive. Since completely distributive lattices are the nuclear objects in the…
We characterize 2-dimensional complexes associated canonically with basis graphs of matroids as simply connected triangle-square complexes satisfying some local conditions. This proves a version of a (disproved) conjecture by Stephen Maurer…
Let $R=\mathbb{K}[X_1, \ldots , X_n ]$ be a polynomial ring over a field $\mathbb{K}$. We introduce an endomorphism $\mathcal{F}^{[m]}: R \rightarrow R $ and denote the image of an ideal $I$ of $R$ via this endomorphism as $I^{[m]}$ and…
We prove model completeness for the theory of addition and the Frobenius map for certain subrings of rational functions in positive characteristic. More precisely: Let $p$ be a prime number, $\mathbb{F}_{p}$ the prime field with $p$…
We prove special cases of a general conjecture: If an invertible field theory admits a projectively topological boundary theory, then it has finite order in the abelian group of invertible field theories. One can substitute `gapped' for…
A submonoid A of N^d has a natural order defined by a <= a + b for elements a and b of A. The Frobenius complex is the order complex of an open interval of A with respect to this order. In this paper, the homotopy type of the Frobenius…
While persistent homology has taken strides towards becoming a wide-spread tool for data analysis, multidimensional persistence has proven more difficult to apply. One reason is the serious drawback of no longer having a concise and…
A new connection between two different necessary conditions for a polymatroid to be linearly representable is presented. Specifically, we prove that the existence of a tensor product with the uniform matroid of rank two on three elements…
Although in general there is no meaningful concept of factorization in fields, that in free associative algebras (over a commutative field) can be extended to their respective free field (universal field of fractions) on the level of…
The purpose of this paper is mostly to present conjectures that extend, to the ``triangular partition'' context (partitions ``under any line'' in the terminology of Blaziak-Haiman-Morse-Pun-Seelinger), properties of Frobenius of…
An infinite family of exactly-solvable and integrable potentials on a plane is introduced. It is shown that all already known rational potentials with the above properties allowing separation of variables in polar coordinates are particular…
We present an algebraic structure in modules over integer rings with cardinality prime powers, which allows to define bases. With such structure, we prove a similar version for the basis extension theorem of linear algebra over fields.…
We show that it makes sense to speak of THE Frobenius manifold attached to a convenient and nondegenerate Laurent polynomial
We introduce a class of k-potential submanifolds in pseudo-Euclidean spaces and prove that for an arbitrary positive integer k and an arbitrary nonnegative integer p, each N-dimensional Frobenius manifold can always be locally realized as…
We prove a duality principle for a special class of submanifolds in pseudo-Euclidean spaces. This class of submanifolds with potential of normals is introduced in this paper. We prove also, for example, that an arbitrary Frobenius manifold…
We study module like objects over categorical quotients of algebras by the action of coalgebras with several objects. These take the form of ``entwined comodules'' and ``entwined contramodules'' over a triple $(\mathscr C,A,\psi)$, where…
Matroid varieties are the closures in the Grassmannian of sets of points defined by specifying which Pl\"ucker coordinates vanish and which don't --- the set of nonvanishing Pl\"ucker coordinates forms a well-studied object called a…