Fixed Points of the Evacuation of Maximal Chains on Fuss Shapes

For a partition $\lambda$ of an integer, we associate $\lambda$ with a slender poset $P$ the Hasse diagram of which resembles the Ferrers diagram of $\lambda$. Let $X$ be the set of maximal chains of $P$. We consider Stanley's involution $\epsilon:X\rightarrow X$, which is extended from Schützenberger's evacuation on linear extensions of a finite poset. We present an explicit characterization of the fixed points of the map $\epsilon:X\rightarrow X$ when $\lambda$ is a stretched staircase or a rectangular shape. Unexpectedly, the fixed points have a nice structure, i.e., a fixed point can be decomposed in half into two chains such that the first half and the second half are the evacuation of each other. As a consequence, we prove anew Stembridge's $q=-1$ phenomenon for the maximal chains of $P$ under the involution $\epsilon$ for the restricted shapes.

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Promotion and Evacuation

The Electronic Journal of Combinatorics ◽

10.37236/75 ◽

2009 ◽

Vol 16 (2) ◽

Cited By ~ 17

Author(s):

Richard P. Stanley

Keyword(s):

Vector Space ◽

Hecke Algebra ◽

Linear Extensions ◽

Linear Transformations ◽

Basic Properties ◽

Finite Poset ◽

Order Ideals ◽

Maximal Chains

Promotion and evacuation are bijections on the set of linear extensions of a finite poset first defined by Schützenberger. This paper surveys the basic properties of these two operations and discusses some generalizations. Linear extensions of a finite poset $P$ may be regarded as maximal chains in the lattice $J(P)$ of order ideals of $P$. The generalizations concern permutations of the maximal chains of a wider class of posets, or more generally bijective linear transformations on the vector space with basis consisting of the maximal chains of any poset. When the poset is the lattice of subspaces of ${\Bbb F}_q^n$, then the results can be stated in terms of the expansion of certain Hecke algebra products.

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The Alternation Hierarchy for the Theory of mu-lattices

BRICS Report Series ◽

10.7146/brics.v7i29.20163 ◽

2000 ◽

Vol 7 (29) ◽

Cited By ~ 2

Author(s):

Luigi Santocanale

Keyword(s):

Fixed Point ◽

Fixed Number ◽

Hierarchy Problem ◽

Explicit Characterization

The alternation hierarchy problem asks whether every mu-term, that is a term built up using also a least fixed point constructor as well as a greatest fixed point constructor, is equivalent to a mu-term where the number of nested fixed point of a different type is bounded by a fixed number. In this paper we give a proof that the alternation hierarchy for the theory of mu-lattices is strict, meaning that such number does not exist if mu-terms are built up from the basic lattice operations and are interpreted as expected. The proof relies on the explicit characterization of free mu-lattices by means of games and strategies.

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A Characterization of Quasi-Metric Completeness in Terms of α–ψ-Contractive Mappings Having Fixed Points

Mathematics ◽

10.3390/math8010016 ◽

2019 ◽

Vol 8 (1) ◽

pp. 16 ◽

Cited By ~ 2

Author(s):

Salvador Romaguera ◽

Pedro Tirado

Keyword(s):

Fixed Point ◽

Fixed Points ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Contractive Mappings ◽

Nonlinear Anal ◽

Contractive Type ◽

Surprising Fact

We obtain a characterization of Hausdorff left K-complete quasi-metric spaces by means of α – ψ -contractive mappings, from which we deduce the somewhat surprising fact that one the main fixed point theorems of Samet, Vetro, and Vetro (see “Fixed point theorems for α – ψ -contractive type mappings”, Nonlinear Anal. 2012, 75, 2154–2165), characterizes the metric completeness.

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w-Distances on Fuzzy Metric Spaces and Fixed Points

Mathematics ◽

10.3390/math8111909 ◽

2020 ◽

Vol 8 (11) ◽

pp. 1909

Author(s):

Salvador Romaguera

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Fixed Points ◽

Point Theorem ◽

Metric Spaces ◽

Fuzzy Metric Spaces ◽

Complete Metric Spaces ◽

Fuzzy Metric

We propose a notion of w-distance for fuzzy metric spaces, in the sense of Kramosil and Michalek, which allows us to obtain a characterization of complete fuzzy metric spaces via a suitable fixed point theorem that is proved here. Our main result provides a fuzzy counterpart of a renowned characterization of complete metric spaces due to Suzuki and Takahashi.

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Characterization of a b-metric space completeness via the existence of a fixed point of Ciric-Suzuki type quasi-contractive multivalued operators and applications

Analele Universitatii Ovidius Constanta - Seria Matematica ◽

10.2478/auom-2019-0001 ◽

2019 ◽

Vol 27 (1) ◽

pp. 5-33 ◽

Cited By ~ 1

Author(s):

Hanan Alolaiyan ◽

Basit Ali ◽

Mujahid Abbas

Keyword(s):

Fixed Point ◽

Fixed Points ◽

Metric Space ◽

Hausdorff Distance ◽

Existence And Uniqueness ◽

Asymptotic Estimate ◽

Metric Spaces ◽

Multivalued Operators ◽

Fixed Point Sets

Abstract The aim of this paper is to introduce Ciric-Suzuki type quasi-contractive multivalued operators and to obtain the existence of fixed points of such mappings in the framework of b-metric spaces. Some examples are presented to support the results proved herein. We establish a characterization of strong b-metric and b-metric spaces completeness. An asymptotic estimate of a Hausdorff distance between the fixed point sets of two Ciric-Suzuki type quasi-contractive multivalued operators is obtained. As an application of our results, existence and uniqueness of multivalued fractals in the framework of b-metric spaces is proved.

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Stability of Real Parametric Polynomial Discrete Dynamical Systems

Discrete Dynamics in Nature and Society ◽

10.1155/2015/680970 ◽

2015 ◽

Vol 2015 ◽

pp. 1-13

Author(s):

Fermin Franco-Medrano ◽

Francisco J. Solis

Keyword(s):

Fixed Point ◽

Fixed Points ◽

Special Function ◽

Real Polynomial ◽

Polynomial Maps ◽

Polynomial Map ◽

Exact Boundary ◽

The Stability ◽

Real Polynomial Maps

We extend and improve the existing characterization of the dynamics of general quadratic real polynomial maps with coefficients that depend on a single parameterλand generalize this characterization to cubic real polynomial maps, in a consistent theory that is further generalized to realmth degree real polynomial maps. In essence, we give conditions for the stability of the fixed points of any real polynomial map with real fixed points. In order to do this, we have introduced the concept ofcanonical polynomial mapswhich are topologically conjugate to any polynomial map of the same degree with real fixed points. The stability of the fixed points of canonical polynomial maps has been found to depend solely on a special function termedProduct Position Functionfor a given fixed point. The values of this product position determine the stability of the fixed point in question, when it bifurcates and even when chaos arises, as it passes through what we have termedstability bands. The exact boundary values of these stability bands are yet to be calculated for regions of type greater than one for polynomials of degree higher than three.

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A new Ф-generalized quasi metric space with some fixed point results and applications

Filomat ◽

10.2298/fil1711157a ◽

2017 ◽

Vol 31 (11) ◽

pp. 3157-3172

Author(s):

Mujahid Abbas ◽

Bahru Leyew ◽

Safeer Khan

Keyword(s):

Fixed Point ◽

Differential Equations ◽

Fixed Points ◽

Periodic Solutions ◽

Metric Space ◽

Delay Differential Equations ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Existence Of Periodic Solutions ◽

Delay Differential

In this paper, the concept of a new ?-generalized quasi metric space is introduced. A number of well-known quasi metric spaces are retrieved from ?-generalized quasi metric space. Some general fixed point theorems in a ?-generalized quasi metric spaces are proved, which generalize, modify and unify some existing fixed point theorems in the literature. We also give applications of our results to obtain fixed points for contraction mappings in the domain of words and to prove the existence of periodic solutions of delay differential equations.

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Coincidence and fixed points for hybrid tangential maps

Georgian Mathematical Journal ◽

10.1515/gmj.2010.013 ◽

2010 ◽

Vol 17 (2) ◽

pp. 273-285

Author(s):

Tayyab Kamran ◽

Quanita Kiran

Keyword(s):

Fixed Point ◽

Fixed Points ◽

Common Property ◽

Fixed Point Theorems ◽

Acta Math ◽

Contractive Condition ◽

The Common

Abstract In [Int. J. Math. Math. Sci. 2005: 3045–3055] by Liu et al. the common property (E.A) for two pairs of hybrid maps is defined. Recently, O'Regan and Shahzad [Acta Math. Sin. (Engl. Ser.) 23: 1601–1610, 2007] have introduced a very general contractive condition and obtained some fixed point results for hybrid maps. We introduce a new property for pairs of hybrid maps that contains the property (E.A) and obtain some coincidence and fixed point theorems that extend/generalize some results from the above-mentioned papers.

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Solution of Some Impulsive Differential Equations via Coupled Fixed Point

Symmetry ◽

10.3390/sym13030501 ◽

2021 ◽

Vol 13 (3) ◽

pp. 501

Author(s):

Ahmed Boudaoui ◽

Khadidja Mebarki ◽

Wasfi Shatanawi ◽

Kamaleldin Abodayeh

Keyword(s):

Fixed Point ◽

Differential Equations ◽

Fixed Points ◽

Metric Space ◽

Fixed Point Theorems ◽

Coupled Fixed Point ◽

Sufficient Conditions ◽

Impulsive Differential Equations ◽

System Of Differential Equations ◽

Coupled Fixed Points

In this article, we employ the notion of coupled fixed points on a complete b-metric space endowed with a graph to give sufficient conditions to guarantee a solution of system of differential equations with impulse effects. We derive recisely some new coupled fixed point theorems under some conditions and then apply our results to achieve our goal.

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Microbrook, Mesobrook, Macrobrook

Perspectives on Public Management and Governance ◽

10.1093/ppmgov/gvz015 ◽

2019 ◽

Vol 2 (4) ◽

pp. 245-253 ◽

Cited By ~ 6

Author(s):

Sebastian Jilke ◽

Asmus Leth Olsen ◽

William Resh ◽

Saba Siddiki

Keyword(s):

Problem Solving ◽

Public Administration ◽

Theory And Practice ◽

Levels Of Analysis ◽

Explicit Characterization ◽

Methodological Perspective ◽

Level Of Analysis ◽

Effective Problem

Abstract This article assesses the field of public administration from a conceptual and methodological perspective. We urge public administration scholars to resolve the ambiguities that mire our scholarship due to the inadequate treatment of levels of analysis in our research. Overall, we encourage methodological accountability through a more explicit characterization of one’s research by the level of analysis to which it relates. We argue that this particular form of accountability is critical for effective problem solving for advancing theory and practice.

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