Related papers: Grothendieck ring of the pairing function without …

Let $Q$ be a commutative, Noetherian ring and $Z \subseteq \operatorname{Spec}(Q)$ a closed subset. Define $K_0^Z(Q)$ to be the Grothendieck group of those bounded complexes of finitely generated projective $Q$-modules that have homology…

Let $G$ be a compact connected Lie group and $P \to M$ a smooth principal $G$-bundle. Let a `cylinder function' on the space $\A$ of smooth connections on $P$ be a continuous function of the holonomies of $A$ along finitely many piecewise…

We establish a bijective correspondence between Smirnov words with balanced letter multiplicities and Hamiltonian paths in complete $m$-partite graphs $K_{n,n,\ldots,n}$. This bijection allows us to derive closed inclusion-exclusion…

An induced packing of cycles in a graph is a set of vertex-disjoint cycles with no edges between them. We generalise the classic Erd\H{o}s-P\'osa theorem to induced packings of cycles. More specifically, we show that there exist functions…

A chord of a cycle $C$ is an edge joining two non-consecutive vertices of $C$. A cycle $C$ in a graph $G$ is chorded if the vertex set of $C$ induces at least one chord. In this paper, we prove that if $G$ is a graph with order $n\geq 6$…

The set of unrestricted homotopy classes $[M,S^n]$ where $M$ is a closed and connected spin $(n+1)$-manifold is called the $n$-th cohomotopy group $\pi^n(M)$ of $M$. Moreover it is known that $\pi^n(M) = H^n(M;\mathbb Z) \oplus \mathbb Z_2$…

We investigate the existence and distribution of Herman rings of transcendental meromorphic functions which have at least one omitted value. If all the poles of such a function are multiple then it has no Herman ring. Herman rings of period…

Let $R$ be a ring with involution $*$ and $Z^*(R)$ denotes the set of all non-zero zero-divisors of $R$. We associate a simple (undirected) graph $\Gamma'(R)$ with vertex set $Z^*(R)$ and two distinct vertices $x$ and $y$ are adjacent in…

Let G be a noncyclic group of order 4, and let K be the ring Z of rational integers, the localization of Z at the prime 2 and the ring of 2-adic integers, respectively. We describe, up to conjugacy, all of the indecomposable subgroups in…

We introduce analogues of Soergel bimodules for complex reflection groups of rank one. We give an explicit parametrization of the indecomposable objects of the resulting category and give a presentation of its split Grothendieck ring by…

Let $R$ be a commutative ring and $M$ be an $R$-module, and let $Z(M)$ be the set of all zero-divisors on $M$. In 2008, D.F. Anderson and A. Badawi introduced the regular graph of $R$. In this paper, we generalize the regular graph of $R$…

We determine the Grothendieck rings of the category of finite-dimensional modules over Queer Lie superalgebras via their rings of characters. In particular, we show that the ring of characters of the Queer Lie supergroup $Q(n)$ is…

Let $f_{F,G}(n)$ be the largest size of an induced $F$-free subgraph that every $n$-vertex $G$-free graph is guaranteed to contain. We prove that for any triangle-free graph $F$, \[ f_{F,K_3}(n) = f_{K_2,K_3}(n)^{1 + o(1)} = n^{\frac{1}{2}…

For $E \subset {\Bbb F}_q^d$, $d \ge 2$, where ${\Bbb F}_q$ is the finite field with $q$ elements, we consider the distance graph ${\mathcal G}^{dist}_t(E)$, $t \not=0$, where the vertices are the elements of $E$, and two vertices $x$, $y$…

We show that the motivic zeta functions of smooth, geometrically connected curves with no rational points are rational functions. This was previously known only for curves whose smooth projective models have a rational point on each…

We prove the following theorem. Let $r\ge 4$ be an integer, and $G$ be a $K_{1,r}$-free $r$-edge-connected $r$-regular graph. Then, for every set $W$ of even number of vertices of $G$ such that the distance between any two vertices of $W$…

A geodesic cycle is a closed curve that connects finitely many points along geodesics. We study geodesic cycles on the sphere in regard to their role in equal-weight quadrature rules and approximation.

Let G be a real, connected, noncompact, semisimple Lie group, let K be a maximal compact subgroup of G, and let g=k+p be the corresponding Cartan decomposition of the complexified Lie algebra of G. Sequences of strongly orthogonal…

We clarify the relationship between Grothendieck duality \`a la Neeman and the Wirthm\"uller isomorphism \`a la Fausk-Hu-May. We exhibit an interesting pattern of symmetry in the existence of adjoint functors between compactly generated…

How hard is it to fill a loop in a Cayley graph with an unoriented surface? Following a comment of Gromov in "Asymptotic invariants of infinite groups", we define homological filling functions of groups with coefficients in a group $R$. Our…