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We study signed differential posets, a signed version of differential posets. These posets satisfy enumerative identities which are signed analogues of those satisfied by differential posets. Our main motivations are the sign-imbalance…

Combinatorics · Mathematics 2007-05-23 Thomas Lam

Recently a new kind of approximation to continuum topological spaces has been introduced, the approximating spaces being partially ordered sets (posets) with a finite or at most a countable number of points. The partial order endows a poset…

q-alg · Mathematics 2008-02-03 Elisa Ercolessi , Giovanni Landi , Paulo Teotonio-Sobrinho

As algebraic semantics of the logic of quantum mechanics there are usually used orthomodular posets, i.e. bounded posets with a complementation which is an antitone involution and where the join of orthogonal elements exists and the…

Rings and Algebras · Mathematics 2019-11-14 Ivan Chajda , Miroslav Kolařík , Helmut Länger

In this paper, we establish a theory of well-posedness for delay differential equations (DDEs) via notions of \textit{prolongations} and \textit{$C^1$-prolongations}, which are continuous and continuously differentiable extensions of…

Classical Analysis and ODEs · Mathematics 2018-10-16 Junya Nishiguchi

The commutative and homological algebra of modules over posets is developed, as closely parallel as possible to the algebra of finitely generated modules over noetherian commutative rings, in the direction of finite presentations, primary…

Commutative Algebra · Mathematics 2020-08-13 Ezra Miller

We explore lattice structures on integer binary relations (i.e. binary relations on the set $\{1, 2, \dots, n\}$ for a fixed integer $n$) and on integer posets (i.e. partial orders on the set $\{1, 2, \dots, n\}$ for a fixed integer $n$).…

Combinatorics · Mathematics 2023-11-14 Grégory Chatel , Vincent Pilaud , Viviane Pons

Coxeter and Dynkin diagrams classify a wide variety of structures, most notably finite reflection groups, lattices having such groups as symmetries, compact simple Lie groups and complex simple Lie algebras. The simply laced or "ADE" Dynkin…

Representation Theory · Mathematics 2026-01-06 John C. Baez

We apply to locally finite partially ordered sets a construction which associates a complete lattice to a given poset; the elements of the lattice are the closed subsets of a closure operator, defined starting from the concurrency relation.…

Logic in Computer Science · Computer Science 2009-11-13 Luca Bernardinello , Lucia Pomello , Stefania Rombolà

The goal of this paper is to prove that several variants of deciding whether a poset can be (weakly) embedded into a small Boolean lattice, or to a few consecutive levels of a Boolean lattice, are NP-complete, answering a question of Griggs…

Discrete Mathematics · Computer Science 2023-06-22 Dömötör Pálvölgyi

In order to be able to use methods of Universal Algebra for investigating posets, we assign to every pseudocomplemented poset, to every relatively pseudocomplemented poset and to every sectionally pseudocomplemented poset a certain algebra…

Rings and Algebras · Mathematics 2021-03-24 Ivan Chajda , Helmut Länger

We prove that the 18-element non-lattice orthomodular poset depicted in the paper is the smallest one and unique up to isomorphism. Since not every Boolean poset is orthomodular, we consider the class of the so-called generalized…

Quantum Algebra · Mathematics 2022-10-12 Ivan Chajda , Miroslav Kolařík , Helmut Länger

We generalize Bj\"{o}rner and Stanley's poset of compositions to $m$-colored compositions. Their work draws many analogies between their (1-colored) composition poset and Young's lattice of partitions, including links to (quasi-)symmetric…

Combinatorics · Mathematics 2007-05-23 Brian Drake , T. Kyle Petersen

Let $\mathcal{C}$ be a small, connected category with finite hom-sets. We show that if the embedding of a connected subcategory $\mathcal{J}$ is both initial and final, then the restriction of any $\mathcal{C}$-module along $\mathcal{J}$…

Representation Theory · Mathematics 2026-04-14 Thomas Brüstle , Justin Desrochers , Samuel Leblanc

In this paper we provide a preliminary investigation of subclasses of bounded posets with antitone involution which are "pastings" of their maximal Kleene sub-lattices. Specifically, we introduce super-paraorthomodular lattices, namely…

Logic · Mathematics 2023-11-13 Davide Fazio , Raffaele Mascella

Given a measurable space (X, M) there is a (Galois) connection between sub-sigma-algebras of M and equivalence relations on X. On the other hand equivalence relations on X are closely related to congruences on stochastic relations. In…

Logic in Computer Science · Computer Science 2010-06-03 Ingo Battenfeld

We study computably enumerable equivalence relations (abbreviated as ceers) under computable reducibility, and we investigate the resulting degree structure Ceers, which is a poset with a smallest and a greatest element. We point out a…

Logic · Mathematics 2018-10-05 Uri Andrews , Andrea Sorbi

It is elementary and well-known that if an element x of a bounded modular lattice L has a complement in L then x has a relative complement in every interval [a,b] containing x. We show that the relatively strong assumption of modularity of…

Combinatorics · Mathematics 2021-07-13 Ivan Chajda , Helmut Länger

M. Busaniche, R. Cignoli, C. Tsinakis and A. M. Wille showed that every residuated lattice induces a residuation on its full twist product. For their construction they used also lattice operations. We generalize this problem to…

Rings and Algebras · Mathematics 2020-12-01 Ivan Chajda , Helmut Länger

The aim of this paper is to study lattice properties of the sharp partial order for complex matrices having index at most 1. We investigate the down-set of a fixed matrix $B$ under this partial order via isomorphisms with two different…

Rings and Algebras · Mathematics 2024-12-30 Cecilia R. Cimadamore , Laura A. Rueda , Néstor Thome , Melina V. Verdecchia

We introduce two new partial orders on the standard Young tableaux of a given partition shape, in analogy with the strong and weak Bruhat orders on permutations. Both posets are ranked by the major index statistic offset by a fixed shift.…

Combinatorics · Mathematics 2020-05-19 Sara C. Billey , Matjaž Konvalinka , Joshua P. Swanson