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In this note, we present a notion of species isomorphism for fibered Burnside rings. We prove that a species isomorphism can be restricted to an isomorphism of mark tables, that it can be extended to an isomorphism between the ghost rings…

Representation Theory · Mathematics 2022-09-26 Benjamín García

We develop new closed form representations of sums of (n + {\alpha})th shifted harmonic numbers and reciprocal binomial coefficients in terms of {\alpha}th shifted harmonic numbers. Some interesting new consequences and illustrative…

Number Theory · Mathematics 2017-03-30 Ce Xu

The square-free word problem relative to a system of two defining relations is decidable.

Logic · Mathematics 2012-03-05 Nikolay L. Poliakov

In this article we provide a simple combinatorial description of morphisms between indecomposable complexes in the bounded derived category of a gentle algebra.

Representation Theory · Mathematics 2015-01-23 Kristin Krogh Arnesen , Rosanna Laking , David Pauksztello

This paper is devoted to a discussion of specific properties of invariants in the theory of forms.

Analysis of PDEs · Mathematics 2010-07-02 Mehdi Nadjafikhah , Parastoo Kabi-Nejad

We introduce several highness notions on degrees related to the problem of computing isomorphisms between structures, provided that isomorphisms exist. We consider variants along axes of uniformity, inclusion of negative information, and…

Logic · Mathematics 2021-09-17 Wesley Calvert , Johanna N. Y. Franklin , Dan Turetsky

A central problem in proof-theory is that of finding criteria for identity of proofs, that is, for when two distinct formal derivations can be taken as denoting the same logical argument. In the literature one finds criteria which are…

Logic · Mathematics 2021-10-07 Paolo Pistone

In this note we study the convergence of recursively defined infinite series. We explore the role of the derivative of the defining function at the origin (if it exists), and develop a comparison test for such series which can be used even…

Classical Analysis and ODEs · Mathematics 2018-03-16 Tamás Forgács , Jack Luong , Joshua Williamson

In this paper we propose a definition of a recurrence relation homomorphism and illustrate our definition with a few examples. We then define the period of a k-th order of linear recurrence relation and deduce certain preliminary results…

Number Theory · Mathematics 2014-09-24 Alexandre Laugier , Manjil P. Saikia

In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones

Functional Analysis · Mathematics 2025-10-28 Murphy E. Egwe , Funke Yusuf

In this expository article we introduce a diagrammatic scheme to represent reverse classes of weights and some of their properties.

Analysis of PDEs · Mathematics 2014-01-14 Sapto Indratno , Diego Maldonado , Sharad Silwal

Computing a morph between two drawings of a graph is a classical problem in computational geometry and graph drawing. While this problem has been widely studied in the context of planar graphs, very little is known about the existence of…

Computational Geometry · Computer Science 2021-05-28 Patrizio Angelini , Michael A. Bekos , Fabrizio Montecchiani , Maximilian Pfister

Structures based on polarities have been used to provide relational semantics for propositional logics that are modelled algebraically by non-distributive lattices with additional operators. This article develops a first order notion of…

Logic · Mathematics 2023-11-08 Robert Goldblatt

In this note we classify sequences according to whether they are morphic, pure morphic, uniform morphic, pure uniform morphic, primitive morphic, or pure primitive morphic, and for each possibility we either give an example or prove that no…

Formal Languages and Automata Theory · Computer Science 2017-11-30 Jean-Paul Allouche , Julien Cassaigne , Jeffrey Shallit , Luca Q. Zamboni

We introduce an equivalence relation, called cobordism, for words and study cobordism invariants of words inspired by methods of low-dimensional topology.

Combinatorics · Mathematics 2008-06-09 Vladimir Turaev

In this note for a topological group $G$, we introduce a bounded subset of $G$ and we find some relationships of this definition with other topological properties of $G$.

Group Theory · Mathematics 2010-03-16 Kazem Haghnejad Azar

We define the affinization of an arbitrary monoidal category $\mathcal{C}$, corresponding to the category of $\mathcal{C}$-diagrams on the cylinder. We also give an alternative characterization in terms of adjoining dot generators to…

Category Theory · Mathematics 2021-11-12 Youssef Mousaaid , Alistair Savage

In this note, we show how a combinatorial identity of Frisch can be applied to prove and generalize some well-known identities involving harmonic numbers. We also present some combinatorial identities involving odd harmonic numbers which…

Combinatorics · Mathematics 2024-08-05 Kunle Adegoke , Robert Frontczak

We give a new, shorter computation of Frobenius push-forwards of line bundles on toric varieties.

Algebraic Geometry · Mathematics 2010-12-13 Piotr Achinger

This paper introduces a notion of decompositions of integral varifolds into countably many integral varifolds, and the existence of such decomposition of integral varifolds whose first variation is representable by integration is…

Differential Geometry · Mathematics 2023-07-26 Hsin-Chuang Chou