Partially ordered set ≈ Partially ordered set
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Generalized Ordered Propositions Fusion Based on Belief Entropy Open
A set of ordered propositions describe the different intensities of a characteristic of an object, the intensities increase or decrease gradually. A basic support function is a set of truth-values of ordered propositions, it includes the d…
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Gamma-positivity in combinatorics and geometry Open
Gamma-positivity is an elementary property that polynomials with symmetric coefficients may have, which directly implies their unimodality. The idea behind it stems from work of Foata, Schützenberger and Strehl on the Eulerian polynomials;…
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Deriving Consensus for Hierarchical Incomplete Ordered Partitions and Coverings Open
A method for determining consensus of hierarchical incomplete ordered partitions and coverings of sets is presented in this chapter. Incomplete ordered partitions and coverings are often used in expert information analysis. These structure…
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Largest acylindrical actions and Stability in hierarchically hyperbolic groups Open
We consider two manifestations of non-positive curvature: acylindrical actions (on hyperbolic spaces) and quasigeodesic stability. We study these properties for the class of hierarchically hyperbolic groups, which is a general framework fo…
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NONCROSSING SETS AND A GRASSMANN ASSOCIAHEDRON Open
We study a natural generalization of the noncrossing relation between pairs of elements in $[n]$ to $k$ -tuples in $[n]$ that was first considered by Petersen et al. [ J. Algebra 324 (5) (2010), 951–969]. We give an alternative approach to…
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Iterative Properties of Birational Rowmotion I: Generalities and Skeletal Posets Open
We study a birational map associated to any finite poset $P$. This map is a far-reaching generalization (found by Einstein and Propp) of classical rowmotion, which is a certain permutation of the set of order ideals of $P$. Classical rowmo…
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Unimodular Equivalence of Order and Chain Polytopes Open
Order polytope and chain polytope are two polytopes that arise naturally from a finite partially ordered set. These polytopes have been deeply studied from viewpoints of both combinatorics and commutative algebra. Even though these polytop…
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Cybersecurity against the Loopholes in Industrial Control Systems Using Interval-Valued Complex Intuitionistic Fuzzy Relations Open
Technology is rapidly advancing and every aspect of life is being digitalized. Since technology has made life much better and easier, so organizations, such as businesses, industries, companies and educational institutes, etc., are using i…
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Theory of interleavings on categories with a flow Open
The interleaving distance was originally defined in the field of Topological Data Analysis (TDA) by Chazal et al. as a metric on the class of persistence modules parametrized over the real line. Bubenik et al. subsequently extended the def…
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Syntactic Conditions for Antichain Property in Consistency Restoring Prolog Open
We study syntactic conditions which guarantee when a CR-Prolog (Consistency Restoring Prolog) program has antichain property: no answer set is a proper subset of another. A notable such condition is that the program's dependency graph bein…
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A Supplier Selection Model for a Wholesaler and Retailer Company Based on FITradeoff Multicriteria Method Open
The problem approached is regarding supplier selection in a wholesaler and retailer of the construction sector. The current approach used in the company analyzed for the supplier selection problem is unable to evaluate the many issues that…
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Residuated relational systems Open
The aim of the present paper is to generalize the concept of residuated poset, by replacing the usual partial ordering by a generic binary relation, giving rise to relational systems which are residuated. In particular, we modify the defin…
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Measuring the sustainable development goals: A poset analysis Open
Sustainability requires balanced development. The economy, society and the environment all need to be pursued simultaneously. In this context, the issue of incomparabilities among different dimensions of indices is at the heart of the disc…
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Combinatorial properties of ultrametrics and generalized ultrametrics Open
Let \\(X\\), \\(Y\\) be sets and let \\(\\Phi\\), \\(\\Psi\\) be mappings with domains \\(X^{2}\\) and \\(Y^{2}\\), respectively. We say that \\(\\Phi\\) and \\(\\Psi\\) are \\emph{combinatorially similar} if there are bijections \\(f \\co…
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Possibility Frames and Forcing for Modal Logic Open
This paper develops the model theory of normal modal logics based on partial “possibilities” instead of total “worlds,” following Humberstone [1981] instead of Kripke [1963]. Possibility semantics can be seen as extending to modal logic th…
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Poset pinball, GKM-compatible subspaces, and Hessenberg varieties Open
This paper has three main goals. First, we set up a general framework to address the problem of constructing module bases for the equivariant cohomology of certain subspaces of GKM spaces. To this end we introduce the notion of a GKM-compa…
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THE EXPECTED JAGGEDNESS OF ORDER IDEALS Open
The jaggedness of an order ideal $I$ in a poset $P$ is the number of maximal elements in $I$ plus the number of minimal elements of $P$ not in $I$ . A probability distribution on the set of order ideals of $P$ is toggle-symmetric if for ev…
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Orlik-Solomon type presentations for the cohomology algebra of toric arrangements Open
We give an explicit presentation for the integral cohomology ring of the complement of any arrangement of level sets of characters in a complex torus (alias “toric arrangement”). Our description parallels the one given by Orlik and Solomon…
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Data structures for real multiparameter persistence modules Open
A theory of modules over posets is developed to define computationally feasible, topologically interpretable data structures, in terms of birth and death of homology classes, for persistent homology with multiple real parameters. To replac…
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A further study on ordered regular equivalence relations in ordered semihypergroups Open
In this paper, we study the ordered regular equivalence relations on ordered semihypergroups in detail. To begin with, we introduce the concept of weak pseudoorders on an ordered semihypergroup, and investigate several related properties. …
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Traces and fractional Sobolev extension domains with variable exponent Open
Assume that Ω ⊂ R n is a bounded domain.We show that under certain regularity assumptions on Ω there exists a linear extension operator from the space W s,p(.,.) (Ω) to W s,p(.,.) (R n ).As an application we study complemented subspaces in…
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Hierarchical Poset Decoding for Compositional Generalization in Language Open
We formalize human language understanding as a structured prediction task where the output is a partially ordered set (poset). Current encoder-decoder architectures do not take the poset structure of semantics into account properly, thus s…
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N∞-operads and associahedra Open
We provide a combinatorial approach to studying the collection of N ∞operads in G-equivariant homotopy theory for G a finite cyclic group of prime power order.In particular, we show that for G = C p n the natural order on the collection of…
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Locales, Nuclei, and Dragalin Frames Open
It is a classic result in lattice theory that a poset is a complete lattice iff it can be realized as fixpoints of a closure operator on a powerset. Dragalin [9,10] observed that a poset is a locale (complete Heyting algebra) iff it can be…
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Two new forms of ordered soft separation axioms Open
The goal of this work is to introduce and study two new types of ordered soft separation axioms, namely soft T i -ordered and strong soft T i -ordered spaces ( i = 0, 1, 2, 3, 4). These two types are formulated with respect to the ordinary…
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Local Cohomology and Stratification Open
We outline an algorithm to recover the canonical (or, coarsest)\nstratification of a given finite-dimensional regular CW complex into cohomology\nmanifolds, each of which is a union of cells. The construction proceeds by\niteratively local…
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Exact Exponential Algorithms for Two Poset Problems Open
Partially ordered sets (posets) are fundamental combinatorial objects with important applications in computer science. Perhaps the most natural algorithmic task, given a size-n poset, is to compute its number of linear extensions. In 1991 …
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On the number of slim, semimodular lattices Open
A lattice L is slim if it is finite and the set of its join-irreducible elements contains no three-element antichain. Slim, semimodular lattices were previously characterized by G. Czédli and E. T. Schmidt as the duals of the lattices cons…
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Optimal Dynamic Treatment Regimes and Partial Welfare Ordering Open
Dynamic treatment regimes are treatment allocations tailored to heterogeneous individuals (e.g., via previous outcomes and covariates). The optimal dynamic treatment regime is a regime that maximizes counterfactual welfare. We introduce a …
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q-Stirling Identities Revisited Open
We give combinatorial proofs of q-Stirling identities using restricted growth words. This includes a poset theoretic proof of Carlitz's identity, a new proof of the q-Frobenius identity of Garsia and Remmel and of Ehrenborg's Hankel q-Stir…