Related papers: Index theory for partial-bijections

We give a general exposition of model theoretic connected components of groups. We show that if a group G has NIP, then there exists the smallest invariant (over some small set) subgroup of G with bounded index (Theorem 5.3). This result…

We extend Borel's theorem on the dominance of word maps from semisimple algebraic groups to some perfect groups. In another direction, we generalize Borel's theorem to some words with constants. We also consider the surjectivity problem for…

In this paper, we establish second main theorems for holomorphic maps with finite growth index on complex discs intersecting families of hypersurfaces (moving and fixed) in projective varieties, where the small term is detailed estimate for…

We prove that finite-index conformal nets are fully dualizable objects in the 3-category of conformal nets. Therefore, assuming the cobordism hypothesis applies, there exists a local framed topological field theory whose value on the point…

We show that every countable set of partial bijections from an infinite set to itself can be obtained as a composition of just two such partial bijections. This strengthens a result by Higgins, Howie, Mitchell and Ru\v{s}kuc stating that…

We focus on working on incidence rings, a class of (possibly infinite) matrix rings indexed by ordered sets. Some general properties about them are given, including how they are always the inverse limit of finite matrix rings, giving a…

We present infinite analogues of our splinter lemma from [Trees of tangles in abstract separation systems, arXiv:1909.09030]. From these we derive several tree-of-tangles-type theorems for infinite graphs and infinite abstract separation…

This is the first of two papers on partition functions and the index theory of transversally elliptic operators. In this paper we only discuss algebraic and combinatorial issues related to partition functions. The applications to index…

In this paper we investigate some strong convergence theorems for partial sums with respect to Vilenkin system.

We introduce a generalized notion of inference system to support more flexible interpretations of recursive definitions. Besides axioms and inference rules with the usual meaning, we allow also coaxioms, which are, intuitively, axioms which…

We define an analytical index map and a topological index map for conical pseudomanifolds. These constructions generalize the analogous constructions used by Atiyah and Singer in the proof of their topological index theorem for a smooth,…

We introduce a new combinatorial object called tower diagrams and prove fundamental properties of these objects. We also introduce an algorithm that allows us to slide words to tower diagrams. We show that the algorithm is well-defined only…

A partial automorphism of a finite graph is an isomorphism between its vertex induced subgraphs. The set of all partial automorphisms of a given finite graph forms an inverse monoid under composition (of partial maps). We describe the…

Irrelevance-based partial MAPs are useful constructs for domain-independent explanation using belief networks. We look at two definitions for such partial MAPs, and prove important properties that are useful in designing algorithms for…

In this paper we introduce the additive analogue of the index of a polynomial over finite fields. We study several problems in the theory of polynomials over finite fields in terms of their additive indices, such as value set sizes, bounds…

Many combinatorial proofs rely on induction. When these proofs are formulated in traditional language, they can be bulky and unmanageable. Coalgebras provide a language which can reduce reduce many inductive proofs in graded poset theory to…

We constructively prove that the partially ordered set of finite permutations ordered by deletion of entries contains an infinite antichain.

We give a K-theory proof of the invariance under cobordism of the family index. We consider elliptic pseudodifferential families on a continuous fibre bundle with smooth fibres over a compact base space B, and define a notion of cobordant…

We determine a strong form of the decomposition theorem for proper toric maps over finite fields.

The main result of this paper is to show that all binomial identities are orderable. This is a natural statement in the combinatorial theory of finite sets, which can also be applied in distributed computing to derive new strong bounds on…