相关论文: On the Number of Rumer Diagrams

We determine the rings of invariants in the symmetric algebra on the dual of a vector space V over the field of two elements, for the group G of orthogonal transformations preserving a non-singular quadratic form on V. The invariant ring is…

We define ruling invariants for even-valence Legendrian graphs in standard contact three-space. We prove that rulings exist if and only if the DGA of the graph, introduced by the first two authors, has an augmentation. We set up the usual…

We study semicontinuous maps on varieties of modules over finite-dimensional algebras. We prove that truncated Euler maps are upper or lower semicontinuous. This implies that $g$-vectors and $E$-invariants of modules are upper…

The purpose of this survey is to provide a gentle introduction to several recent breakthroughs in graph Ramsey theory. In particular, we will outline the proofs (due to various groups of authors) of exponential improvements to the diagonal,…

We present bases for certain spaces of meromorphic vector-valued rational-weight mock modular forms constructed using Rademacher sums.

This note generalizes a result contained in a previous paper [ J. Sanders, Circuit preserving edge maps II, J. Combin. Theory Ser. B 42 (1987), 146-155].

Let k be an algebraically closed field of characteristic p>0. We compute the Weyl filtration multiplicities in indecomposable tilting modules and the decomposition numbers for the general linear group over k in terms of cap diagrams under…

Using algebraic transformations and equivalent reformulations we derive a number of new results from some earlier ones (by the author) in more accepted terms closely related to well-known conjectures of Bondy and Jung including a number of…

We close a gap appearing at the same time in the author's thesis "Iterated rings of bounded elements and generalizations of Schm\"udgen's theorem" [1] and in the author's article "Iterated rings of bounded elements and generalizations of…

Maps from links in thickened surfaces to flat-virtual links help to construct invariants of links using invariants of flat-virtual links. This work is dedicated to investigation of equivalence and invariants of flat-virtual diagrams…

We present an algebraic theory of orthogonal polynomials in several variables that includes classical orthogonal polynomials as a special case. Our bottom line is a straightforward connection between apolarity of binary forms and the inner…

We give a characterisation of the idempotents of the partition monoid, and use this to enumerate the idempotents in the finite partition, Brauer and partial Brauer monoids, giving several formulae and recursions for the number of…

Inspired by recent works on rings satisfying Auslander's conjecture, we study invariants, which we call Auslander bounds, and prove that they have strong relations to some homological conjectures.

We analyze a notion of multiple valued sections of a vector bundle over an abstract smooth Riemannian manifold, which was suggested by W. Allard in the unpublished note "Some useful techniques for dealing with multiple valued functions" and…

This is a graduate-level introduction to graph theory, corresponding to a quarter-long course. It covers simple graphs, multigraphs as well as their directed analogues, and more restrictive classes such as tournaments, trees and…

This paper introduces a novel framework for constructing invariants in $G$-equivariant birational geometry by unifying two recent approaches: the theory of atoms recently developed by Katzarkov, Kontsevich, Pantev, and Yu, and the theory of…

We study multisymplectic structures taking values in vector bundles with connections from the viewpoint of the Hamiltonian symmetry. We introduce the notion of bundle-valued $n$-plectic structures and exhibit some properties of them. In…

We study the classical invariant theory of the Bezoutiant R(A,B) of a pair of binary forms A,B. It is shown that R(A,B) admits a Taylor expansion whose coefficients are (essentially) the odd transvectants (A,B)_{2r+1}. Moreover, R(A,B) is…

Let G be a finite group acting on a finite dimensional real vector space V. We denote by P(V) the projective space associated to V. In this paper we compute in a very explicit way the rank of the equivariant complex K-theory of V and P(V),…

We consider word maps and word maps with constants on a simple algebraic group. We present results on the images of such maps, in particular, we prove a theorem on the dominance of general word maps with constants, which can be viewed as an…