Related papers: On finitization of the Gordon identities

Let $A$ and $B$ be finite-dimensional simple algebras with arbitrary signature over an algebraically closed field. Suppose $A$ and $B$ are graded by a semigroup $S$ so that the graded identitical relations of $A$ are the same as those of…

For a fixed odd prime $\ell$, we present new families of identities defined on various subposets of the poset of isomorphism classes of finite abelian $\ell$-groups, generalizing identities of Hall and Cohen-Lenstra. We also present a…

We generalize Wagoner's representation of the automorphism group of a two-sided subshifts of finite type as the fundamental group of a certain CW-complex to groupoids having a certain refinement structure. This significantly streamlines the…

We prove the theorems which are equivalent to the Roland's results such that a new form of them allows to consider some generalizations. In particular, we give generators of primes more than a fixed prime.

We prove metric rigidity for complete manifolds supporting solutions of certain second order differential systems, thus extending classical works on a characterization of space-forms. In the route, we also discover new characterizations of…

Let $F$ be a finite field with characteristic $p > 2$ and let $G$ be the unitary Grassmann algebra generated by an infinite dimensional vector space $V$ over $F$. In this paper, we determine a basis of the $\mathbb{Z}_{2}$-graded polynomial…

We extend the short presentation due to [Borel '53] of the cohomology ring of a generalized flag manifold to a relatively short presentation of the cohomology of any of its Schubert varieties. Our result is stated in a root-system uniform…

We prove a q-series identity that generalises Macdonald's A_{2n}^{(2)} eta-function identity and the Rogers-Ramanujan identities. We conjecture our result to generalise even further to also include the Andrews-Gordon identities.

We show that if an open cover of a finite dimensional space is equivariant with respect to some finite group action on the space then there is an equivariant refinement of bounded dimension. This will generalize some constructions of…

We study centralisers of finite order automorphisms of generalisations of Thompson's group F and conjugacy classes of finite subgroups in finite extensions of these groups. In particular, we show that centralisers of finite automorphisms in…

The paper aims to generalize Clausen's identity to the square of any Gauss hypergeometric function. Accordingly, solutions of the related 3rd order linear differential equation are found in terms of certain bivariate series that can reduce…

We show that given a face of Hironaka's characteristic polyhedron, it does only depend on the singularity and a flag defined by the linear form determining the face. As a consequence we get that certain numerical data obtained from the…

We study the family of Y-systems and T-systems associated with the sine-Gordon models and the reduced sine-Gordon models for the parameter of continued fractions with two terms. We formulate these systems by cluster algebras, which turn out…

We state and prove a general summation identity. The identity is then applied to derive various summation formulas involving the generalized harmonic numbers and related quantities. Interesting results, mostly new, are obtained for both…

We use geometric algebra techniques to give a synthetic and computationally efficient approach to Fierz identities in arbitrary dimensions and signatures, thus generalizing previous work. Our approach leads to a formulation which displays…

According to the method of series rearrangement, we establish two generalizations of Andrews' curious $q$-series identity with an extra integer parameter. The limiting cases of them produce two extensions of Andrews' curious…

We prove a generalization of the polarization identity of linear algebra expressing the inner product of a complex inner product space in terms of the norm, where the field of scalars is extended to an associative algebra equipped with an…

We give explicit formulae and study the combinatorics of an identity holding in all Rota-Baxter algebras. We describe the specialization of this identity for a couple of examples of Rota-Baxter algebras.

This paper is a direct generalization of Baker-Bowler theory to flag matroids, including its moduli interpretation as developed by Baker and the second author for matroids. More explicitly, we extend the notion of flag matroids to flag…

We introduce the notion of flag Bott-Samelson variety as a generalization of Bott-Samelson variety and flag variety. Using a birational morphism from an appropriate Bott-Samelson variety to a flag Bott-Samelson variety, we compute…