scholarly journals On the evaluation of the Tutte polynomial at the points (1,-1) and (2,-1)

2011 ◽  
Vol DMTCS Proceedings vol. AO,... (Proceedings) ◽  
Author(s):  
Andrew Goodall ◽  
Criel Merino ◽  
Anna de Mier ◽  
Marc Noy
Keyword(s):  
Complete Graph ◽  
Tutte Polynomial ◽  
Sufficient Condition ◽  
Bijective Proof ◽  
Nous Permet ◽  
Threshold Graphs ◽  
International Audience ◽  
Identity Based ◽  
The Relationship ◽  
Cette Condition

International audience C. Merino [Electron. J. Combin. 15 (2008)] showed that the Tutte polynomial of a complete graph satisfies $t(K_{n+2};2,-1)=t(K_n;1,-1)$. We first give a bijective proof of this identity based on the relationship between the Tutte polynomial and the inversion polynomial for trees. Next we move to our main result, a sufficient condition for a graph G to have two vertices u and v such that $t(G;2,-1)=t(G-\{u,v\};1,-1)$; the condition is satisfied in particular by the class of threshold graphs. Finally, we give a formula for the evaluation of $t(K_{n,m};2,-1)$ involving up-down permutations. C. Merino [Electron. J. Combin. 15 (2008)] a montré que le polynôme de Tutte du graphe complet satisfait $t(K_{n+2};2,-1)=t(K_n;1,-1)$. Le rapport entre le polynôme de Tutte et le polynôme d'inversions d'un arbre nous permet de donner une preuve bijective de cette identité. Le résultat principal du travail est une condition suffisante pour qu'un graphe ait deux sommets u et v tels que $t(G;2,-1)=t(G-\{u,v\};1,-1)$; en particulier, les graphes ``threshold'' satisfont cette condition. Finalement, nous donnons une formule pour $t(K_{n,m};2,-1)$ qui fait intervenir les permutations alternées.

scholarly journals Cayley and Tutte polytopes

2012 ◽  
Vol DMTCS Proceedings vol. AR,... (Proceedings) ◽  
Author(s):  
Matjaž Konvalinka ◽  
Igor Pak
Keyword(s):  
Complete Graph ◽  
Tutte Polynomial ◽  
Convex Hulls ◽  
Connected Graphs ◽  
Labeled Trees ◽  
Graph Traversal ◽  
International Audience ◽  
Search Graph ◽  
Traversal Algorithm

International audience Cayley polytopes were defined recently as convex hulls of Cayley compositions introduced by Cayley in 1857. In this paper we resolve Braun's conjecture, which expresses the volume of Cayley polytopes in terms of the number of connected graphs. We extend this result to a two-variable deformations, which we call Tutte polytopes. The volume of the latter is given via an evaluation of the Tutte polynomial of the complete graph. Our approach is based on an explicit triangulation of the Cayley and Tutte polytope. We prove that simplices in the triangulations correspond to labeled trees and forests. The heart of the proof is a direct bijection based on the neighbors-first search graph traversal algorithm. Les polytopes de Cayley ont été définis récemment comme des ensembles convexes de compositions de Cayley introduits par Cayley en 1857. Dans ce papier, nous résolvons la conjecture de Braun. Cette dernière exprime le volume du polytopes de Cayley en termes du nombre de graphes connexes. Nous étendons ce résultat à des déformations de polytopes de Cayley à deux variables, à savoir les polytopes de Tutte. Le volume de ces derniers est donnè par une évaluation du polynôme de Tutte du graphe complet. Notre approche est basée sur une triangulation explicite des polytopes de Cayley et Tutte. Nous démontrons que les simplexes de ces triangulations correspondent à des arbres marqués. La pierre angulaire de notre démonstration est une bijection directe basées sur l'algorithme de la recherche du premier voisin sur le graphe.

Contractual Relationships among Artists, Record Labels, and Artist Management Companies in Japan

2020 ◽  
Author(s):  
Kazuhiro Ando
Keyword(s):  
Music Industry ◽  
Music Business ◽  
Know How ◽  
Contractual Relationships ◽  
The World ◽  
Employee Relationship ◽  
International Audience ◽  
Music Market ◽  
Japanese Music ◽  
The Relationship

Although Japan is the second largest music market in the world, the structure and practices of the music industry are little understood internationally. People overseas need to know how the music business works in Japan so that they can conduct business comfortably. The Japanese music industry has unique features in some respects. First, Japanese record labels remain heavily dependent on traditional physically packaged music although its profitability is much lower than that of digital distribution. Second, full-scale competition in the music copyright management business has just begun. While JASRAC monopolized this market for more than sixty years, the new entrant, NexTone has gradually increased the market share thanks to the frustration experienced by many music publishers and songwriters in their dealings with JASRAC. Third, the relationship between artists and artist management companies is more like an employer-employee relationship than a client-agent relationship. Artist management companies are fully invested in discovering, nurturing, and marketing young artists just the way big businesses handle their recruits. This chapter illuminates practices of the Japanese music industry for an international audience.

Are misinformation, antiscientific claims, and conspiracy theories for political extremists?

2021 ◽  
Vol 24 (4) ◽  
pp. 583-605
Author(s):  
Adam M. Enders ◽  
Joseph E. Uscinski
Keyword(s):  
The Political ◽  
Conspiracy Theories ◽  
Political Orientations ◽  
Conspiracy Beliefs ◽  
Political Left ◽  
Identity Based ◽  
Nationally Representative ◽  
The Relationship ◽  
Political Groups ◽  
Representative Samples

Extremist political groups, especially “extreme” Republicans and conservatives, are increasingly charged with believing misinformation, antiscientific claims, and conspiracy theories to a greater extent than moderates and those on the political left by both a burgeoning scholarly literature and popular press accounts. However, previous investigations of the relationship between political orientations and alternative beliefs have been limited in their operationalization of those beliefs and political extremity. We build on existing literature by examining the relationships between partisan and nonpartisan conspiracy beliefs and symbolic and operational forms of political extremity. Using two large, nationally representative samples of Americans, we find that ideological extremity predicts alternative beliefs only when the beliefs in question are partisan in nature and the measure of ideology is identity-based. Moreover, we find that operational ideological extremism is negatively related to nonpartisan conspiracy beliefs. Our findings help reconcile discrepant findings regarding the relationship between political orientations and conspiracy beliefs.

On derivatives of fuzzy multi-dimensional mappings and applications under generalized differentiability

2021 ◽  
pp. 1-19
Author(s):  
M. Miri Karbasaki ◽  
M. R. Balooch Shahriari ◽  
O. Sedaghatfar
Keyword(s):  
Linear Function ◽  
Level Set ◽  
Fuzzy Numbers ◽  
Sufficient Condition ◽  
Continuous Linear ◽  
Generalized Differentiability ◽  
Relationship Of ◽  
The Relationship ◽  
Derivatives Of ◽  
Dimensional Mapping

This article identifies and presents the generalized difference (g-difference) of fuzzy numbers, Fréchet and Gâteaux generalized differentiability (g-differentiability) for fuzzy multi-dimensional mapping which consists of a new concept, fuzzy g-(continuous linear) function; Moreover, the relationship between Fréchet and Gâteaux g-differentiability is studied and shown. The concepts of directional and partial g-differentiability are further framed and the relationship of which will the aforementioned concepts are also explored. Furthermore, characterization is pointed out for Fréchet and Gâteaux g-differentiability; based on level-set and through differentiability of endpoints real-valued functions a characterization is also offered and explored for directional and partial g-differentiability. The sufficient condition for Fréchet and Gâteaux g-differentiability, directional and partial g-differentiability based on level-set and through employing level-wise gH-differentiability (LgH-differentiability) is expressed. Finally, to illustrate the ability and reliability of the aforementioned concepts we have solved some application examples.

scholarly journals Toeplitz Operators on the Bergman Space of Planar Domains with Essentially Radial Symbols

2011 ◽  
Vol 2011 ◽  
pp. 1-26 ◽  
Author(s):  
Roberto C. Raimondo
Keyword(s):  
Bergman Space ◽  
Toeplitz Operators ◽  
Boundary Behavior ◽  
Berezin Transform ◽  
Planar Domain ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Planar Domains ◽  
Necessary And Sufficient ◽  
The Relationship

We study the problem of the boundedness and compactness of when and is a planar domain. We find a necessary and sufficient condition while imposing a condition that generalizes the notion of radial symbol on the disk. We also analyze the relationship between the boundary behavior of the Berezin transform and the compactness of

scholarly journals The Quality Of Leader/Employee Relationship

2006 ◽  
Vol 4 (2) ◽  
Author(s):  
F. J. Carstens ◽  
Neil Barnes
Keyword(s):  
South Africa ◽  
Decision Making ◽  
Business Performance ◽  
Business Leaders ◽  
Research Approach ◽  
Sufficient Condition ◽  
Employee Relationship ◽  
The Relationship

This study set out to investigate what role the quality of the relationship between business leaders and their employees played in the performance of their business. The study compared the business performance of forty-five area managers in one of the major listed banks in South Africa with their specific leader/employee relationship profiles. The research approach was quantitative and of a correlational nature. The results indicate that although certain elements within the relationship between business leaders and employees indeed have an influence on business performance this alone was not a sufficient condition. The study suggested that the dimensions relating to vision, trust, accountability and decision- making have the strongest influence on business performance. Further research in this area is suggested.

The Maxslope Taxometric Procedure: Mathematical Derivation, Parameter Estimation, Consistency Tests

2004 ◽  
Vol 95 (2) ◽  
pp. 517-550 ◽  
Author(s):  
William M. Grove
Keyword(s):  
Parameter Estimation ◽  
Nonlinear Regression ◽  
Classification Accuracy ◽  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Indicator Variable ◽  
Regression Slope ◽  
The Relationship ◽  
Mathematical Derivation ◽  
Made In

This article first explains concepts in taxometrics, including the meaning of “taxon” in relation to taxometric procedures. It then mathematically develops the MAXSLOPE procedure of Grove and Meehl which relies on nonlinear regression of one taxometric indicator variable on another. Sufficient conditions for MAXSLOPE's validity are set forth. The relationship between the point of maximum regression slope (MAXSLOPE point) and the HITMAX cut, i.e., the point on a variable which, if used as a diagnostic cut-off score, yields maximum classification accuracy, is analyzed. A sufficient condition is given for the MAXSLOPE point to equal the HITMAX cut; however, most distributions have different MAXSLOPE and HITMAX points. Equations and an algorithm are spelled out for making a graphical test for the existence of a taxon, estimating taxometric parameters, and conducting consistency tests; the latter serve as stringent checks on the validity of a taxonic conjecture. The plausibility of assumptions made, in deriving MAXSLOPE equations, is discussed, and the qualitative effects of violations of these assumptions are explained.

scholarly journals A direct bijective proof of the hook-length formula

1997 ◽  
Vol Vol. 1 ◽  
Author(s):  
Jean-Christophe Novelli ◽  
Igor Pak ◽  
Alexander V. Stoyanovskii
Keyword(s):  
Young Tableaux ◽  
Hook Length ◽  
Bijective Proof ◽  
International Audience ◽  
Standard Young Tableaux

International audience This paper presents a new proof of the hook-length formula, which computes the number of standard Young tableaux of a given shape. After recalling the basic definitions, we present two inverse algorithms giving the desired bijection. The next part of the paper presents the proof of the bijectivity of our construction. The paper concludes with some examples.

scholarly journals Q-borderenergetic threshold graphs

2020 ◽  
Vol 42 ◽  
pp. e91
Author(s):  
João Roberto Lazzarin ◽  
Oscar Franscisco Másquez Sosa ◽  
Fernando Colman Tura
Keyword(s):  
Complete Graph ◽  
Threshold Graphs ◽  
Laplacian Energy ◽  
Signless Laplacian

A graph G is said to be borderenergetic (L-borderenergetic, respectively) if its energy (Laplacian energy, respectively) equals the energy (Laplacian energy, respectively) of the complete graph. Recently, this concept was extend to signless Laplacian energy (see Tao, Q., Hou, Y. (2018). Q-borderenergetic graphs. AKCE International Journal of Graphs and Combinatorics). A graph G is called Q-borderenergetic if its signless Laplacian energy is the same of the complete graph Kn; i.e., QE(G) = QE(Kn) = 2n - 2: In this paper, we investigate Q-borderenergetic graphs on the class of threshold graphs. For a family of threshold graphs of order n = 100; we find out exactly 13 graphs such that QE(G) = 2n- 2:

scholarly journals Generalized approximate boundary synchronization for a coupled system of wave equations

2020 ◽  
Author(s):  
Yanyan Wang
Keyword(s):  
Wave Equations ◽  
Dirichlet Boundary ◽  
Coupled System ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Exact Boundary ◽  
Boundary Controls ◽  
The Relationship ◽  
Exact Boundary Synchronization ◽  
Dirichlet Boundary Controls

In this paper, we consider the generalized approximate boundary synchronization for a coupled system of wave equations with Dirichlet boundary controls. We analyse the relationship between the generalized approximate boundary synchronization and the generalized exact boundary synchronization, give a sufficient condition to realize the generalized approximate boundary synchronization and a necessary condition in terms of Kalman’s matrix, and show the meaning of the number of total controls. Besides, by the generalized synchronization decomposition, we define the generalized approximately synchronizable state, and obtain its properties and a sufficient condition for it to be independent of applied boundary controls.

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