scholarly journals Enumeration of Cylindric Plane Partitions

2012 ◽  
Vol DMTCS Proceedings vol. AR,... (Proceedings) ◽  
Author(s):  
Robin Langer
Keyword(s):  
Natural Generalization ◽  
Path Model ◽  
Plane Partition ◽  
Combinatorial Interpretation ◽  
Plane Partitions ◽  
Generating Series ◽  
International Audience ◽  
The Individual ◽  
The Right ◽  
Reverse Plane

International audience Cylindric plane partitions may be thought of as a natural generalization of reverse plane partitions. A generating series for the enumeration of cylindric plane partitions was recently given by Borodin. As in the reverse plane partition case, the right hand side of this identity admits a simple factorization form in terms of the "hook lengths'' of the individual boxes in the underlying shape. The first result of this paper is a new bijective proof of Borodin's identity which makes use of Fomin's growth diagram framework for generalized RSK correspondences. The second result of this paper is a $(q,t)$-analog of Borodin's identity which extends previous work by Okada in the reverse plane partition case. The third result of this paper is an explicit combinatorial interpretation of the Macdonald weight occurring in the $(q,t)$-analog in terms of the non-intersecting lattice path model for cylindric plane partitions. Les partitions planes cylindriques sont une généralisation naturelle des partitions planes renversées. Une série génératrice pour énumération des partitions planes cylindriques a été donnée récemment par Borodin. Comme dans le cas des partitions planes renversées, la partie droite de cette identité peut être factoriser en terme de "longueur d’équerres'' des carrés dans la forme sous-jacente. Le premier résultat de cet article est une nouvelle preuve bijective de l'identité de Borodin qui utilise le cadre de "diagramme de croissance'' de Fomin pour la correspondance de RSK généralisée. Le deuxième résultat de cette article est une $(q,t)$-déformation d'identité de Borodin qui généralise un résultat de Okada dans le cas des partitions planes renversées. Le troisième résultat de cet article est une formule combinatoire explicite pour le poids de Macdonald qui utilise le modèle des chemins non-intersectant pour les partitions planes cylindriques.

scholarly journals The expansion of Hall-Littlewood functions in the dual Grothendieck polynomial basis

2010 ◽  
Vol DMTCS Proceedings vol. AN,... (Proceedings) ◽  
Author(s):  
Jason Bandlow ◽  
Jennifer Morse
Keyword(s):  
Symmetric Functions ◽  
Polynomial Basis ◽  
Dual Basis ◽  
Nous Obtenons ◽  
Plane Partitions ◽  
Generalize Charge ◽  
Littlewood Polynomials ◽  
International Audience ◽  
Reverse Plane ◽  
Grothendieck Polynomials

International audience A combinatorial expansion of the Hall-Littlewood functions into the Schur basis of symmetric functions was first given by Lascoux and Schützenberger, with their discovery of the charge statistic. A combinatorial expansion of stable Grassmannian Grothendieck polynomials into monomials was first given by Buch, using set-valued tableaux. The dual basis of the stable Grothendieck polynomials was given a combinatorial expansion into monomials by Lam and Pylyavskyy using reverse plane partitions. We generalize charge to set-valued tableaux and use all of these combinatorial ideas to give a nice expansion of Hall-Littlewood polynomials into the dual Grothendieck basis. \par En associant une charge à un tableau, une formule combinatoire donnant le développement des polynômes de Hall-Littlewood en termes des fonctions de Schur a été obtenue par Lascoux et Schützenberger. Une formule combinatoire donnant le développement des polynômes de Grothendieck Grassmanniens stables en termes des fonctions monomiales a quant à elle été obtenue par Buch à l'aide de tableaux à valeurs sur des ensembles. Finalement, une formule faisant intervenir des partitions planaires inverses a été obtenue par Lam et Pylyavskyy pour donner le développement de la base duale aux polynômes de Grothendieck stables en termes de monômes. Nous généralisons le concept de charge aux tableaux à valeurs sur des ensembles et, en nous servant de toutes ces notions combinatoires, nous obtenons une formule élégante donnant le développement des polynômes de Hall-Littlewood en termes de la base de Grothendieck duale.

scholarly journals Tableaux combinatorics for two-species PASEP probabilities

2015 ◽  
Vol DMTCS Proceedings, 27th... (Proceedings) ◽  
Author(s):  
Olya Mandelshtam
Keyword(s):  
Steady State ◽  
Stationary Distribution ◽  
Heavy Particle ◽  
Finite Lattice ◽  
Nous Proposons ◽  
Combinatorial Interpretation ◽  
One Dimensional ◽  
International Audience ◽  
The Right ◽  
Steady State Probabilities

International audience The goal of this paper is to provide a combinatorial expression for the steady state probabilities of the twospecies PASEP. In this model, there are two species of particles, one “heavy” and one “light”, on a one-dimensional finite lattice with open boundaries. Both particles can hop into adjacent holes to the right and left at rates 1 and $q$. Moreover, when the heavy and light particles are adjacent to each other, they can switch places as if the light particle were a hole. Additionally, the heavy particle can hop in and out at the boundary of the lattice. Our first result is a combinatorial interpretation for the stationary distribution at $q=0$ in terms of certain multi-Catalan tableaux. We provide an explicit determinantal formula for the steady state probabilities, as well as some general enumerative results for this case. We also describe a Markov process on these tableaux that projects to the two-species PASEP, and hence directly explains the connection between the two. Finally, we extend our formula for the stationary distribution to the $q=1$ case, using certain two-species alternative tableaux. Le but de ce document est de fournir une expression combinatoire décrivant les probabilités de l’état d’équilibre de PASEP à deux espèces. Dans ce modèle, il existe deux espèces de particules, une “lourde” et une “légère”, disposées sur un réseau fini unidimensionnel. Les deux particules peuvent sauter dans les trous adjacents à droite et à gauche, avec des probabilités proportionnelles à 1 et $q$. Par ailleurs, lorsque les particules lourdes et légères sont à côté l’une de l’autre, elles peuvent changer de place, comme si la particule légère était un trou. En outre, la particule lourde peut sauter dans et hors de la frontière du réseau. Notre premier résultat est une interprétation combinatoire de la distribution stationnaire dans le cas $q=0$, en termes de certains tableaux “multi-Catalan”. Nous proposons une formule explicite déterminantale pour les probabilités stationnaires, ainsi que plusieurs résultats énumératifs généraux pour ce cas. Nous décrivons aussi un processus de Markov sur ces tableaux, qui se projette sur le PASEP à deux espèces, et qui fournit donc directement une connexion entre les deux. Enfin, nous exprimons notre formule pour la distribution stationnaire dans le cas $q=1$, en utilisant certains tableaux alternatifs de deux espèces.

scholarly journals An Involution Principle-Free Bijective Proof of Stanley's Hook-Content Formula

1998 ◽  
Vol Vol. 3 no. 1 ◽  
Author(s):  
Christian Krattenthaler
Keyword(s):  
Generating Function ◽  
Plane Partitions ◽  
Bijective Proof ◽  
International Audience ◽  
Reverse Plane

International audience A bijective proof for Stanley's hook-content formula for the generating function for column-strict reverse plane partitions of a given shape is given that does not involve the involution principle of Garsia and Milne. It is based on the Hillman-Grassl algorithm and Schützenberger's \emphjeu de taquin.

scholarly journals Refined dual stable Grothendieck polynomials and generalized Bender-Knuth involutions

2020 ◽  
Vol DMTCS Proceedings, 28th... ◽  
Author(s):  
Pavel Galashin ◽  
Darij Grinberg ◽  
Gaku Liu
Keyword(s):  
Symmetric Functions ◽  
Schur Functions ◽  
The Other ◽  
Countable Family ◽  
Plane Partitions ◽  
International Audience ◽  
K Theory ◽  
Reverse Plane ◽  
Grothendieck Polynomials

International audience The dual stable Grothendieck polynomials are a deformation of the Schur functions, originating in the study of the K-theory of the Grassmannian. We generalize these polynomials by introducing a countable family of additional parameters such that the generalization still defines symmetric functions. We outline two self-contained proofs of this fact, one of which constructs a family of involutions on the set of reverse plane partitions generalizing the Bender-Knuth involutions on semistandard tableaux, whereas the other classifies the structure of reverse plane partitions with entries 1 and 2.

Boundaries of Restricting the Rights of Human and Citizen

2020 ◽  
Vol 26 (2) ◽  
pp. 232-236
Author(s):  
Manol Stanin
Keyword(s):  
Negative Impact ◽  
The Individual ◽  
The Right ◽  
Positive Results

AbstractLimitation of rights is a measure proved its effectiveness with positive results for the community in war, military or another emergency.Attitude to rightsmust be human with a view to the right-to-human relationshipbecause the crossing of a certain boundary leads to a disintegration of rights and a negative impact on the personality.This implies necessity from legal institutionalization of clear criteria to refine the limitation of rights, both for the purpose of their protection and for the purpose of protecting the individual.

Tourism as a Tool for the Fulfilment of the Rights to Rest and Leisure Enshrined in Article No. 24 of the Universal Declaration of Human Rights

2019 ◽  
Vol 76 (3-4) ◽  
pp. 180-188
Author(s):  
Bianca Nicla Romano
Keyword(s):  
Human Rights ◽  
Legal System ◽  
Universal Declaration ◽  
Title V ◽  
Negative Consequences ◽  
Real Right ◽  
Right To Work ◽  
The Individual ◽  
The Right ◽  
Italian Constitution

Art. 24 of the 1948 Declaration of Human Rights recognises and protects the right of the individual to rest and leisure. This right has to be fully exercised without negative consequences on the right to work and the remuneration. Tourism can be considered one of the best ways of rest and leisure because it allows to enrich the personality of the individual. Even after the reform of the Title V this area is no longer covered by the Italian Constitution, the Italian legal system protects and guarantees it as a real right, so as to get to recognize its existence and the consequent compensation of the so-called “ruined holiday damage”. This kind of damage has not a patrimonial nature, but a moral one, and the Tourist-Traveler can claim for it when he has not been able to fully enjoy his holiday - the essential fulcrum of tourism - intended as an opportunity for leisure and/or rest, essential rights of the individual.

VALUE EDUCATION SYSTEM IN INDIA

2019 ◽  
Vol 8 (1) ◽  
Author(s):  
Jyoti Narayan Patra ◽  
Jayanta Mete
Keyword(s):  
Education System ◽  
Personality Development ◽  
The Family ◽  
The Individual ◽  
The Right

Values are like seeds that sprout, become saplings, grow into trees and spread their branches all around. To be able to think right, to feel the right kind of emotions and to act in the desirable manner are the prime phases of personality development. Building up of values system starts with the individual, moves on to the family and community, reorienting systems, structures and institutions, spreading throughout the land and ultimately embracing the planet as a whole. The culture of inclusivity is particularly relevant and important in the context of our society, nation and making education a right for all children.

Ayurveda dietary guidelines during Covid-19 Pandemic

2020 ◽  
Vol 11 (SPL1) ◽  
pp. 1477-1481
Author(s):  
Ishwari Gaikwad ◽  
Priyanka Shelotkar
Keyword(s):  
Dietary Habits ◽  
Relevant Literature ◽  
Dietary Guidelines ◽  
The Body ◽  
Daily Regimen ◽  
Web Page ◽  
Healthy State ◽  
Health Disorders ◽  
The Individual ◽  
The Right

The current world situation is both frightening and alarming due to the massive disruption caused by the Covid-19 pandemic. The next few days are censorious as we need to be very precautious in our daily regimen as well as dietary habits. Ayurveda offers knowledge about food based on certain reasoning. Indecent food custom is the chief cause for the rising development of health disorders in the current era. In classical texts of Ayurveda, the concept of diet explained well, ranging from their natural sources, properties and specific utility in pathological as well as physiological manner. In this work, the review of the relevant literature of Ahara (Diet) was carried out from Charak Samhita and other texts, newspapers, articles, web page related to the same.  Every human being is unique with respect to his Prakriti (Physical and mental temperament), Agni (Digestive capacity), Koshtha  (Nature of bowel) etc. For that reason, the specificity of the individual should be kept in mind. Ahara, when consumed in the appropriate amount at the right moment following all Niyamas (Guidelines) given in Ayurveda texts, gives immunity and keeps the body in a healthy state during pandemics such as Covid-19. Ultimately, this will help the human body to maintain its strength for life. This article reviews the concept of diet viz. combination of foods, their quantity and quality, methods of preparation and processing, which are to be followed during pandemics and are essential in maintenance and endorsement of health and preclusion of diseases.

Fulfilling the Right to Food for South Africa: Justice, Security, Sovereignty and the Politics of Malnutrition

2020 ◽  
Vol 11 (3) ◽  
pp. 112-152
Author(s):  
Busiso Helard Moyo ◽  
Anne Marie Thompson Thow
Keyword(s):  
South Africa ◽  
Food Systems ◽  
Food System ◽  
Food Sovereignty ◽  
Food Justice ◽  
System Transformation ◽  
Right To Food ◽  
Economic Rights ◽  
The Individual ◽  
The Right

Despite South Africa’s celebrated constitutional commitments that have expanded and deepened South Africa’s commitment to realise socio-economic rights, limited progress in implementing right to food policies stands to compromise the country’s developmental path. If not a deliberate policy choice, the persistence of hunger, food insecurity and malnutrition in all its forms is a deep policy failure.  Food system transformation in South Africa requires addressing wider issues of who controls the food supply, thus influencing the food chain and the food choices of the individual and communities. This paper examines three global rights-based paradigms – ‘food justice’, ‘food security’ and ‘food sovereignty’ – that inform activism on the right to food globally and their relevance to food system change in South Africa; for both fulfilling the right to food and addressing all forms of malnutrition. We conclude that the emerging concept of food sovereignty has important yet largely unexplored possibilities for democratically managing food systems for better health outcomes.

Chimeras In Time-Honored Societies

Think India ◽  
2019 ◽  
Vol 22 (2) ◽  
pp. 463-466
Author(s):  
TUMMALA. SAI MAMATA
Keyword(s):  
Major Elements ◽  
The Sun ◽  
Human Beings ◽  
Life Changes ◽  
Inner Self ◽  
The World ◽  
Nature And Nurture ◽  
The Individual ◽  
The Right ◽  
Superstitious Beliefs

A river flows serenely accepting all the miseries and happiness that it comes across its journey. A tree releases oxygen for human beings despite its inner plights. The sun is never tired of its duty and gives sunlight without any interruption. Why are all these elements of nature so tuned to? Education is knowledge. Knowledge comes from learning. Learning happens through experience. Familiarity is the master of life that shapes the individual. Every individual learns from nature. Nature teaches how to sustain, withdraw and advocate the prevailing situations. Some dwell into the deep realities of nature and nurture as ideal human beings. Life is a puzzle. How to solve it is a million dollar question that can never be answered so easily. The perception of life changes from individual to individual making them either physically powerful or feeble. Society is not made of only individuals. Along with individuals it has nature, emotions, spiritual powers and superstitious beliefs which bind them. Among them the most crucial and alarming is the emotions which are interrelated to others. Alone the emotional intelligence is going to guide the life of an individual. For everyone there is an inner self which makes them conscious of their deeds. The guiding force should always force the individual to choose the right path.  Writers are the powerful people who have rightly guided the society through their ingenious pen outs.  The present article is going to focus on how the major elements bound together are dominating the individual’s self through Rabindranath Tagore’s Home and the World (1916)

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