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The goal of this note is to compare two notions, one coming from the theory of rewrite systems and the other from proof theory: confluence and cut elimination. We show that to each rewrite system on terms, we can associate a logical system:…

Logic in Computer Science · Computer Science 2023-05-24 Gilles Dowek

In this paper we present a new approach to Morse theory based on the de Rham-Federer theory of currents. The full classical theory is derived in a transparent way. The methods carry over uniformly to the equivariant and the holomorphic…

Differential Geometry · Mathematics 2012-08-27 F. Reese Harvey , H. Blaine Lawson,

One of the most basic facts related to the famous Ulam reconstruction conjecture is that the connectedness of a graph can be determined by the deck of its vertex-deleted subgraphs, which are considered up to isomorphism. We strengthen this…

Computational Complexity · Computer Science 2024-06-14 V. Arvind , Johannes Köbler , Oleg Verbitsky

Deduction systems and graph rewriting systems are compared within a common categorical framework. This leads to an improved deduction method in diagrammatic logics.

Logic in Computer Science · Computer Science 2010-11-10 Dominique Duval

This article is a survey of conjectures and results on reductive algebraic groups having good reduction at a suitable set of discrete valuations of the base field. Until recently, this subject has received relatively little attention, but…

Number Theory · Mathematics 2020-08-18 Andrei S. Rapinchuk , Igor A. Rapinchuk

The confluence of untyped \lambda-calculus with unconditional rewriting is now well un- derstood. In this paper, we investigate the confluence of \lambda-calculus with conditional rewriting and provide general results in two directions.…

Logic in Computer Science · Computer Science 2011-09-21 Frédéric Blanqui , Claude Kirchner , Colin Riba

Completion is one of the most studied techniques in term rewriting and fundamental to automated reasoning with equalities. In this paper we present new correctness proofs of abstract completion, both for finite and infinite runs. For the…

Logic in Computer Science · Computer Science 2023-06-22 Nao Hirokawa , Aart Middeldorp , Christian Sternagel , Sarah Winkler

Deformation theory is treated for locally notherian formal schemes (non necessarily smooth). The cotangent complex is defined in the derived category through the homology localization functor. The basic properties and results of a…

Algebraic Geometry · Mathematics 2024-02-06 Marta Pérez Rodríguez

We define term rewriting systems on the vertices and faces of nestohedra, and show that the former are confluent and terminating. While the associated posets on vertices generalize Barnard--McConville's flip order for graph-associahedra,…

Category Theory · Mathematics 2025-01-22 Pierre-Louis Curien , Guillaume Laplante-Anfossi

We present intersection type systems in the style of sequent calculus, modifying the systems that Valentini introduced to prove normalisation properties without using the reducibility method. Our systems are more natural than Valentini's…

Logic in Computer Science · Computer Science 2015-03-18 Kentaro Kikuchi

We show that diagrammatic sets, a topologically sound alternative to polygraphs and strict $\omega$-categories, admit an internal notion of equivalence in the sense of coinductive weak invertibility. We prove that equivalences have the…

Category Theory · Mathematics 2025-12-23 Clémence Chanavat , Amar Hadzihasanovic

Several general properties, concerning reduction algebras - rings of definition and algorithmic efficiency of the set of ordering relations - are discussed. For the reduction algebras, related to the diagonal embedding of the Lie algebra…

Representation Theory · Mathematics 2009-12-22 Sergey Khoroshkin , Oleg Ogievetsky

A \emph{locally irregular graph} is a graph whose adjacent vertices have distinct degrees. We say that a graph $G$ can be decomposed into $k$ locally irregular subgraphs if its edge set may be partitioned into $k$ subsets each of which…

Combinatorics · Mathematics 2017-03-02 Jakub Przybyło

A theory is developed which uses "networks" (directed acyclic graphs with some extra structure) as a formalism for expressions in multilinear algebra. It is shown that this formalism is valid for arbitrary PROPs (short for 'PROducts and…

Rings and Algebras · Mathematics 2012-04-12 Lars Hellström

We formulate and prove a chain level descent property of symplectic cohomology for involutive covers by compact subsets that take into account the natural algebraic structures that are present. The notion of an involutive cover is reviewed.…

Symplectic Geometry · Mathematics 2025-05-01 Umut Varolgunes

The first author proved that the harmonic convolution of a normalized right half-plane mapping with either another normalized right half-plane mapping or a normalized vertical strip mapping is convex in the direction of the real axis.…

Complex Variables · Mathematics 2009-03-10 Michael Dorff , Maria Nowak , Magdalena Woloszkiewicz

We study incremental stability and convergence of switched (bimodal) Filippov systems via contraction analysis. In particular, by using results on regularization of switched dynamical systems, we derive sufficient conditions for convergence…

Systems and Control · Computer Science 2020-03-18 Mario di Bernardo , Davide Fiore , S. John Hogan

In this paper we study for the incompressible Euler equations the global structure of the bifurcation diagram for the rotating doubly connected patches near the degenerate case. We show that the branches with the same symmetry merge forming…

Analysis of PDEs · Mathematics 2017-10-11 Taoufik Hmidi , Coralie Renault

In this note, we examine the bundle picture of the pullback construction of Lie algebroids. The notion of submersions by Lie algebroids is introduced, which leads to a new proof of the local normal form for lie algebroid transversals of…

Symplectic Geometry · Mathematics 2019-02-20 Pedro Frejlich

The relationship between Term Graph Rewriting and Term Rewriting is well understood: a single term graph reduction may correspond to several term reductions, due to sharing. It is also known that if term graphs are allowed to contain…

Logic in Computer Science · Computer Science 2011-02-15 Andrea Corradini , Frank Drewes