scholarly journals Counting permutations by congruence class of major index

2007 ◽  
Vol 39 (2) ◽  
pp. 269-281
Author(s):  
Hélène Barcelo ◽  
Bruce E. Sagan ◽  
Sheila Sundaram
Keyword(s):  
Congruence Class ◽  
Major Index

Congruence relations on almost distributive lattices-II

2019 ◽  
pp. 2150005
Author(s):  
Gezahagne Mulat Addis
Keyword(s):  
Distributive Lattice ◽  
Congruence Relation ◽  
Congruence Class ◽  
Distributive Lattices ◽  
Ideal Formula ◽  
Congruence Relations

For a given ideal [Formula: see text] of an almost distributive lattice [Formula: see text], we study the smallest and the largest congruence relation on [Formula: see text] having [Formula: see text] as a congruence class.

scholarly journals SUMS OF PRODUCTS OF CONGRUENCE CLASSES AND OF ARITHMETIC PROGRESSIONS

2009 ◽  
Vol 05 (04) ◽  
pp. 625-634
Author(s):  
SERGEI V. KONYAGIN ◽  
MELVYN B. NATHANSON
Keyword(s):  
Arithmetic Progression ◽  
Congruence Class ◽  
Arithmetic Progressions ◽  
Sum Of Products ◽  
Sums Of Products ◽  
Positive Integers ◽  
Congruence Classes

Consider the congruence class Rm(a) = {a + im : i ∈ Z} and the infinite arithmetic progression Pm(a) = {a + im : i ∈ N0}. For positive integers a,b,c,d,m the sum of products set Rm(a)Rm(b) + Rm(c)Rm(d) consists of all integers of the form (a+im) · (b+jm)+(c+km)(d+ℓm) for some i,j,k,ℓ ∈ Z. It is proved that if gcd (a,b,c,d,m) = 1, then Rm(a)Rm(b) + Rm(c)Rm(d) is equal to the congruence class Rm(ab+cd), and that the sum of products set Pm(a)Pm(b)+Pm(c)Pm eventually coincides with the infinite arithmetic progression Pm(ab+cd).

Characteristics analysis of behavioural portfolio theory in the Markowitz portfolio theory framework

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Saksham Mittal ◽  
Sujoy Bhattacharya ◽  
Satrajit Mandal
Keyword(s):  
Emerging Markets ◽  
Asset Allocation ◽  
Portfolio Theory ◽  
Optimal Portfolio ◽  
Content Type ◽  
Major Index ◽  
Brics Countries ◽  
Trade Offs ◽  
Characteristics Analysis ◽  
Mean Variance

PurposeIn recent times, behavioural models for asset allocation have been getting more attention due to their probabilistic modelling for scenario consideration. Many investors are thinking about the trade-offs and benefits of using behavioural models over conventional mean-variance models. In this study, the authors compare asset allocations generated by the behavioural portfolio theory (BPT) developed by Shefrin and Statman (2000) against the Markowitz (1952) mean-variance theory (MVT).Design/methodology/approachThe data used have been culled from BRICS countries' major index constituents from 2009 to 2019. The authors consider a single period economy and generate future probable outcomes based on historical data in order to determine BPT optimal portfolios.FindingsThis study shows that a fair number of portfolios satisfy the first entry constraint of the BPT model. BPT optimal portfolio exhibits high risk and higher returns as compared to typical Markowitz optimal portfolio.Originality/valueThe BRICS countries' data were used because the dynamics of the emerging markets are significantly different from the developed markets, and many investors have been considering emerging markets as their new investment avenues.

scholarly journals Congruence Class Sizes in Finite Sectionally Complemented Lattices

2004 ◽  
Vol 47 (2) ◽  
pp. 191-205 ◽  
Author(s):  
G. Grätzer ◽  
E. T. Schmidt
Keyword(s):  
Congruence Class ◽  
Typical Result ◽  
Complemented Lattices ◽  
The Family ◽  
Complemented Lattice ◽  
Congruence Classes

AbstractThe congruences of a finite sectionally complemented lattice L are not necessarily uniform (any two congruence classes of a congruence are of the same size). To measure how far a congruence Θ of L is from being uniform, we introduce Spec Θ, the spectrum of Θ, the family of cardinalities of the congruence classes of Θ. A typical result of this paper characterizes the spectrum S = (mj | j < n) of a nontrivial congruence Θ with the following two properties:

scholarly journals Deformations of reducible Galois representations to Hida-families

2021 ◽  
pp. 1-24
Author(s):  
Anwesh Ray
Keyword(s):  
Deformation Theory ◽  
Galois Representations ◽  
Congruence Class ◽  
Representation Formula ◽  
Theoretic Approach ◽  
Hida Families ◽  
Global Deformation

The global deformation theory of residually reducible Galois representations with fixed auxiliary conditions is studied. We show that [Formula: see text] lifts to a Hida line for which the weights range over a congruence class modulo-[Formula: see text]. The advantage of the purely Galois theoretic approach is that it allows us to construct [Formula: see text]-adic families of Galois representations lifting the actual representation [Formula: see text], and not just the semisimplification.

scholarly journals Las Elecciones Olvidadas: Reflexiones En Torno A La Participación Ciudadana Locales En El Estado De Hidalgo (1993-2005)

Xihmai ◽  
2012 ◽  
Vol 2 (4) ◽  
Author(s):  
Enrique López Rivera
Keyword(s):  
The State ◽  
Major Index ◽  
Present Text

Resumen Las elecciones de diputados locales son las que concentran el mayor í­ndice de abstencionismo en el estado de Hidalgo. Ese comportamiento puede ser explicado a través de algunos factores de corte sociodemográfico que ayudan a comprender los contrastes y contradicciones de la conducta del votante y del abstencionista. ¿Cuáles de factores ayudan a entender con mayor precisión este fenómeno? Esa es la pregunta que trata de contestar el presente texto. Abstract The elections of local deputies are those that concentrate the major index of abstentionism in the state of Hidalgo. This behavior can be made clear across some factors of court sociodemográfico that they help to understand the contrasts and contradictions of the conduct of the voter and of the abstentionist. Which of factors do help to understand with major precision this phenomenon? This it is the question that tries to answer the present text.

scholarly journals ACDC: Analysis of Congruent Diversification Classes

2022 ◽  
Author(s):  
Sebastian Hoehna ◽  
Bjoern Tore Kopperud ◽  
Andrew F Magee
Keyword(s):  
Congruence Class ◽  
R Package ◽  
Rate Function ◽  
Diversification Rate ◽  
Extinction Rate ◽  
Diversification Rates ◽  
Common Features ◽  
Alternative Hypotheses ◽  
Rate Functions ◽  
Congruence Classes

Diversification rates inferred from phylogenies are not identifiable. There are infinitely many combinations of speciation and extinction rate functions that have the exact same likelihood score for a given phylogeny, building a congruence class. The specific shape and characteristics of such congruence classes have not yet been studied. Whether speciation and extinction rate functions within a congruence class share common features is also not known. Instead of striving to make the diversification rates identifiable, we can embrace their inherent non-identifiable nature. We use two different approaches to explore a congruence class: (i) testing of specific alternative hypotheses, and (ii) randomly sampling alternative rate function within the congruence class. Our methods are implemented in the open-source R package ACDC (https://github.com/afmagee/ACDC). ACDC provides a flexible approach to explore the congruence class and provides summaries of rate functions within a congruence class. The summaries can highlight common trends, i.e. increasing, flat or decreasing rates. Although there are infinitely many equally likely diversification rate functions, these can share common features. ACDC can be used to assess if diversification rate patterns are robust despite non-identifiability. In our example, we clearly identify three phases of diversification rate changes that are common among all models in the congruence class. Thus, congruence classes are not necessarily a problem for studying historical patterns of biodiversity from phylogenies.

scholarly journals Statistics on Lattice Walks and q-Lassalle Numbers

2015 ◽  
Vol DMTCS Proceedings, 27th... (Proceedings) ◽  
Author(s):  
Lenny Tevlin
Keyword(s):  
Positive Integer ◽  
Generating Function ◽  
Catalan Numbers ◽  
Binomial Coefficients ◽  
Integer Coefficients ◽  
Major Index ◽  
Lattice Walks ◽  
International Audience ◽  
The Difference ◽  
Positive Integers

International audience This paper contains two results. First, I propose a $q$-generalization of a certain sequence of positive integers, related to Catalan numbers, introduced by Zeilberger, see Lassalle (2010). These $q$-integers are palindromic polynomials in $q$ with positive integer coefficients. The positivity depends on the positivity of a certain difference of products of $q$-binomial coefficients.To this end, I introduce a new inversion/major statistics on lattice walks. The difference in $q$-binomial coefficients is then seen as a generating function of weighted walks that remain in the upper half-plan. Cet document contient deux résultats. Tout d’abord, je vous propose un $q$-generalization d’une certaine séquence de nombres entiers positifs, liés à nombres de Catalan, introduites par Zeilberger (Lassalle, 2010). Ces $q$-integers sont des polynômes palindromiques à $q$ à coefficients entiers positifs. La positivité dépend de la positivité d’une certaine différence de produits de $q$-coefficients binomial.Pour ce faire, je vous présente une nouvelle inversion/major index sur les chemins du réseau. La différence de $q$-binomial coefficients est alors considérée comme une fonction de génération de trajets pondérés qui restent dans le demi-plan supérieur.

scholarly journals MODEL FOR RAPID ASSESSMENT OF VULNERABILITY OF OFFICE BUILDINGS TO BLAST USING SWARA AND SMART METHODS (A CASE STUDY OF SWISS RE TOWER)

2016 ◽  
Vol 22 (6) ◽  
pp. 831-843 ◽  
Author(s):  
Jalal NAKHAEI ◽  
Mahdi BITARAFAN ◽  
Shahin LALE AREFI ◽  
Oleg KAPLIŃSKI
Keyword(s):  
Rapid Assessment ◽  
Office Buildings ◽  
Architectural Form ◽  
Major Index ◽  
World Demand ◽  
Medium Level ◽  
Four Levels ◽  
And Function ◽  
Building Form

Accidental and intentional explosions are incidents often destroying buildings and leaving casualties. As a re­sult of these blasts all over the world, demand of safe constructions with less vulnerability to explosions is rising. A large number of office buildings are built each year in many countries, housing large numbers of staff and clients, and due to specific nature and function, activities and services, these buildings are usually centrally located. Their architectural form being vital, therefore the article attempts, firstly, to present indices depicting the building form from the viewpoint of vulnerability to explosion. Secondly, the article presents such indexes as: capability to reduce blast effects, economic factors, simplicity of implementation, relationship among spaces in the crisis condition, and creating the least unusable space. The model of rapid assessment of vulnerability of office buildings forms to blast, SMART (simple multi attribute ranking technique) procedure is used and, applying the SWARA method, the weight of each major index and sub-index is arrived at. The model presented in the paper shows the assessment systems using figures between zero and a hundred, and four levels of vulnerability: weak, medium, good and excellent. The closer the figure to a hundred, the lower the vulnerability of the office building forms to blast. Swiss Re Tower case study was presented in the article rating of vul­nerability of this building against explosion. It was found to be equal to 62.11%, and its standing was at medium level.

scholarly journals Asymptotic normality of the major index on standard tableaux

2020 ◽  
Vol 113 ◽  
pp. 101972 ◽  
Author(s):  
Sara C. Billey ◽  
Matjaž Konvalinka ◽  
Joshua P. Swanson
Keyword(s):  
Asymptotic Normality ◽  
Major Index
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