scholarly journals Enumeration on Row-Increasing Tableaux of Shape $2 \times n$

10.37236/8087 ◽  
2019 ◽  
Vol 26 (1) ◽  
Author(s):  
Rosena R.X. Du ◽  
Xiaojie Fan ◽  
Yue Zhao
Keyword(s):  
Major Index ◽  
Schröder Numbers ◽  
Cyclic Sieving

Recently O. Pechenik studied the cyclic sieving of increasing tableaux of shape $2\times n$, and obtained a polynomial on the major index of these tableaux, which is a $q$-analogue of refined small Schröder numbers. We define row-increasing tableaux and study the major index and amajor index of row-increasing tableaux of shape $2 \times n$. The resulting polynomials are both $q$-analogues of refined large Schröder numbers. For both results we give bijective proofs.

scholarly journals Refined cyclic sieving on words for the major index statistic

2018 ◽  
Vol 73 ◽  
pp. 37-60 ◽  
Author(s):  
Connor Ahlbach ◽  
Joshua P. Swanson
Keyword(s):  
Major Index ◽  
Cyclic Sieving

scholarly journals Cyclic sieving for longest reduced words in the hyperoctahedral group

2010 ◽  
Vol DMTCS Proceedings vol. AN,... (Proceedings) ◽  
Author(s):  
T. K. Petersen ◽  
L. Serrano
Keyword(s):  
Generating Function ◽  
Hyperoctahedral Group ◽  
Cyclic Action ◽  
Orbit Structure ◽  
Cyclic Sieving Phenomenon ◽  
Major Index ◽  
Nous Montrons ◽  
International Audience ◽  
Cyclic Sieving ◽  
Cette Action

International audience We show that the set $R(w_0)$ of reduced expressions for the longest element in the hyperoctahedral group exhibits the cyclic sieving phenomenon. More specifically, $R(w_0)$ possesses a natural cyclic action given by moving the first letter of a word to the end, and we show that the orbit structure of this action is encoded by the generating function for the major index on $R(w_0)$. Nous montrons que l'ensemble $R(w_0)$ des expressions réduites pour l'élément le plus long du groupe hyperoctaédral présente le phénomène cyclique de tamisage. Plus précisément, $R(w_0)$ possède une action naturelle cyclique donnée par le déplacement de la première lettre d'un mot vers la fin, et nous montrons que la structure d'orbite de cette action est codée par la fonction génératrice pour l'indice majeur sur $R(w_0)$.

scholarly journals Cyclic Sieving for Longest Reduced Words in the Hyperoctahedral Group

10.37236/339 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
T. Kyle Petersen ◽  
Luis Serrano
Keyword(s):  
Generating Function ◽  
Hyperoctahedral Group ◽  
Cyclic Action ◽  
Orbit Structure ◽  
Cyclic Sieving Phenomenon ◽  
Major Index ◽  
Cyclic Sieving ◽  
Reduced Words

We show that the set $R(w_0)$ of reduced expressions for the longest element in the hyperoctahedral group exhibits the cyclic sieving phenomenon. More specifically, $R(w_0)$ possesses a natural cyclic action given by moving the first letter of a word to the end, and we show that the orbit structure of this action is encoded by the generating function for the major index on $R(w_0)$.

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 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 The Cyclic Sieving Phenomenon for Non-Crossing Forests

10.37236/2419 ◽  
2012 ◽  
Vol 19 (3) ◽  
Author(s):  
Stefan Kluge
Keyword(s):  
Cyclic Group ◽  
Cyclic Sieving Phenomenon ◽  
Cyclic Sieving

In this paper we prove that the set of non-crossing forests together with a cyclic group acting on it by rotation and a natural q-analogue of the formula for their number exhibits the cyclic sieving phenomenon, as conjectured by Alan Guo.

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.

Some properties of the Schröder numbers

2016 ◽  
Vol 47 (4) ◽  
pp. 717-732 ◽  
Author(s):  
Feng Qi ◽  
Xiao-Ting Shi ◽  
Bai-Ni Guo
Keyword(s):  
Schröder Numbers

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.

Sign in / Sign up

Export Citation Format

Share Document