scholarly journals Lecture Hall Partitions and the Affine Hyperoctahedral Group

10.37236/7201 ◽  
2018 ◽  
Vol 25 (1) ◽  
Author(s):  
Christopher R. H. Hanusa ◽  
Carla D. Savage
Keyword(s):  
Generating Function ◽  
The Other ◽  
Lecture Hall ◽  
Hyperoctahedral Group ◽  
Lecture Hall Partitions ◽  
New View

In 1997 Bousquet-Mélou and Eriksson introduced lecture hall partitions as the inversion vectors of elements of the parabolic quotient $\widetilde{C}/C$.  We provide a new view of their correspondence that allows results in one domain to be translated into the other.  We determine the equivalence between combinatorial statistics in each domain and use this correspondence to translate certain generating function formulas on lecture hall partitions to new observations about $\widetilde{C}/C$.

scholarly journals The Geometry of Lecture Hall Partitions and Quadratic Permutation Statistics

2010 ◽  
Vol DMTCS Proceedings vol. AN,... (Proceedings) ◽  
Author(s):  
Katie L. Bright ◽  
Carla D. Savage
Keyword(s):  
Weyl Group ◽  
Generating Function ◽  
Lecture Hall ◽  
Permutation Statistics ◽  
Linear Statistics ◽  
Joint Distributions ◽  
Open Questions ◽  
International Audience ◽  
Lecture Hall Partitions ◽  
Special Case

International audience We take a geometric view of lecture hall partitions and anti-lecture hall compositions in order to settle some open questions about their enumeration. In the process, we discover an intrinsic connection between these families of partitions and certain quadratic permutation statistics. We define some unusual quadratic permutation statistics and derive results about their joint distributions with linear statistics. We show that certain specializations are equivalent to the lecture hall and anti-lecture hall theorems and another leads back to a special case of a Weyl group generating function that "ought to be better known.'' Nous regardons géométriquement les partitions amphithéâtre et les compositions planétarium afin de résoudre quelques questions énumératives ouvertes. Nous découvrons un lien intrinsèque entre ces familles des partitions et certaines statistiques quadratiques de permutation. Nous définissons quelques statistiques quadratiques peu communes des permutations et dérivons des résultats sur leurs distributions jointes avec des statistiques linéaires. Nous démontrons que certaines spécialisations sont équivalentes aux théorèmes amphithéâtre et planétarium. Une autre spécialisation mène à un cas spécial de la série génératrice d'un groupe de Weyl qui "devrait être mieux connue''.

UNIVERSALITAS KETAUHIDAN TUHAN

2020 ◽  
Vol 15 (2) ◽  
pp. 379-403
Author(s):  
Roudhotul Jannah
Keyword(s):  
Oral Communication ◽  
The Other ◽  
Objective Data ◽  
Negotiation Strategy ◽  
Written Text ◽  
Comprehensive Information ◽  
Islamic Religion ◽  
New View ◽  
Qur'anic Interpretation

This article is about Angelika Neuwirth’s thought, dialectical of Qur’anic interpretation. She offer new view to understanding of Qur’an’s meaning. Neuwirth encourage to reunderstanding Qur’an post-canonization (a written text) with pre-canonization method (oral communication), as in Surat Al-Ikhlas. Accourding Neuwirth, Surat Al-Ikhlas responded from tradition and civilization of Arabic region earlier. An example أَحَدٌ (Q.112:1) is similiar meaning with “ehad” in Ibrani language. That’s mean usage أَحَدٌ had purpose to negotiation strategy and universality of faith. therefore Islamic religion has mission to combine all ideology of faith become unity universality. Neuwirth encourages to refer to the other holy scripture for adding comprehensive information and objective data.

scholarly journals Financial and Non-Financial Aspects of Entrepreneurship - the Polish Perspective

2021 ◽  
Vol 17 (4) ◽  
pp. 105-119
Author(s):  
Karolina PalimĄka
Keyword(s):  
Young People ◽  
The Other ◽  
Standard Of Living ◽  
Entrepreneurial Attitudes ◽  
The Subject ◽  
Positive Motivation ◽  
Starting A Business ◽  
New View

Abstract The phenomenon of entrepreneurship has various perspectives – economic, financial, social, and psychological. The aim of this paper is to present entrepreneurship from a perspective merging both financial and non-financial aspects of this phenomenon. The article presents two (complementary) aspects related to the phenomenon of entrepreneurship. One of the aspects described by author is the availability of financing for businesses in Poland (showing the issue in response to the most important obstacle to running a business), the other is shaping entrepreneurial attitudes. The section on sources of financing give an answer to the question of whether (and if so - to what extent) the problem of access to financing is a real barrier to starting a business in Poland. Presenting the perspective of students gives a new view on the subject and enables us to recognize factors that determine the decision to start a business among young people, knowledge of which may contribute to a change in attitudes towards setting up a business in Poland. Among the conclusions, the author mentions, inter alia, the need to strengthen entrepreneurial attitudes among students, especially due to the growing number of companies operating in Poland for reasons of positive motivation (such as improvement of the standard of living or independence). Moreover, the conducted analyses lead to the conclusion that new companies are financed primarily from their own resources, which discourages many from starting their own business.

A note on the time-dependent and the stationary behaviour of a semi-infinite reservoir subject to a combination of Markovian inflows

1971 ◽  
Vol 8 (04) ◽  
pp. 708-715 ◽  
Author(s):  
Emlyn H. Lloyd
Keyword(s):  
Functional Equation ◽  
Explicit Formula ◽  
Generating Function ◽  
Present Theory ◽  
The Other ◽  
Time Dependent ◽  
Independent Sequence ◽  
Time Dependent Solution ◽  
Infinite Reservoir ◽  
Stationary Behaviour

The present theory of finite reservoirs is not rich in general theorems even when of the simple Moran type, with unit draft and stationary discrete independent-sequence inflows. For the corresponding systems with unbounded capacity however there are two classes of results which have been known for some time. One of these classes is concerned with the time-dependent solution, where the theory provides a functional equation for the generating function of the time to first emptiness (Kendall (1957)), and the other with the asymptotic stationary distribution of reservoir contents, for which an explicit formula for the generating function is available (Moran (1959)).

scholarly journals Godsleer en skrifleer: Fokus en uitdaging

2012 ◽  
Vol 46 (2) ◽  
Author(s):  
Callie F.C. Coetzee
Keyword(s):  
South Africa ◽  
The Other ◽  
Current Debate ◽  
Word Of God ◽  
Full Agreement ◽  
Knowledge Of God ◽  
The Bible ◽  
Scientific System ◽  
And Task ◽  
New View

Die keuse van die onderwerp vir hierdie artikel moet teen ‘n bepaalde agtergrond gesien word. In die eerste plek het  dit om die plek en taak van die dogmatiek, waarin die Godsleer en die Skrifleer ‘n besondere plek inneem, gegaan. Dogmatiek is immers die wetenskaplike sisteem van die kennis van God, en God openbaar Hom in besonder deur die Skrif. In die tweede plek het dit oor die aktualiteit van die onderwerp gegaan. Daar word vandag toenemend gepleit vir ‘n nuwe Godsbeeld, wat God se verhouding tot die wêreld betref. Die begrip wat gebruik  word is panenteïsme. Wat die Skrifleer betref, is die vraag na die gesag van die Skrif voortdurend aan die orde. Wat die begrip panenteïsme betref (God in alles en alles in God), in onderskeid van die begrippe deïsme, panteïsme en teïsme, is vanuit die Skrif bevind dat daar geen ineenvloeiing van God en die geskape werklikheid  is, soos die voorstanders van panenteïsme (o.a. die Nuwe Hervorming en Julian Müller in Suid-Afrika) bepleit het nie. Wat die Skrifleer betref, het die debat weereens, soos in die 16de eeu, saamgetrek in die vraag of die Bybel die Woord van God is of die ervaring van mense. Die skrywer se eie standpunt het saamgetrek in volledige instemming met die Gereformeerde belydenis soos verwoord in Nederlandse Geloofsbelydenis, Artikel 2–7. Die voorstanders van ‘n nuwe Godsbeeld (panenteïsme) het egter in hulle Skrifleer radikaal  van die Reformatoriese tradisie afgewyk. Die fokus en uitdaging vir die Gereformeerde dogmatiek lê in die onverswakte handhawing van die Goddelike gesag van die Woord. In sy Woord openbaar God Homself as die transendente en immanente God (teïsme). Hierdie waarheid het onder andere besondere implikasies vir die leer van die voorsienigheid. Wanneer die dogmatiek, in samewerking met ander relevante teologiese dissiplines en die wetenskap van die wysbegeerte en literatuurwetenskap sy taak verrig, eindig ware teologie in doksologie.Doctrine on God and doctrine on Scripture: Focus and challenge. The choice of the title for this article must be seen against a specific background. In the first place it had to do with the place and task of dogmatics, in which the doctrine on God and the doctrine on Scripture are most important. Dogmatics can be defined as the scientific system of the knowledge of God and God reveals Himself in particular in Scripture. Secondly,  it had to do with the actuality of the topic. In the current debate there is an emphasis on a new view of God as far as his relationship with creation is concerned. The term used is panentheism. And as far as the doctrine on Scripture is concerned, the question of the authority of Scripture is always on the agenda. As far as the term panentheism (all in God and God in all) is concerned, distinguished from deism, pantheism and theism, it was concluded that in Scripture we do not find any identity or fusion between God and creation, as the advocates for panentheism (the New Reformers and Julian Müller inter alia in South Africa) plead. As far as the doctrine of Scripture is concerned, the focus is on the question whether the Bible is the Word of God or the experience of man. The author of this article found himself in full agreement with the Reformed confession as formulated in the Belgic Confession, Articles 2–7. On the other hand,  the advocates for a new view about God (panentheism) deviate radically from the Reformed tradition. The focus and challenge for Reformed dogmatics lie in the maintaining of the Divine authority of Scripture. In his Word, God reveals Himself as both the transcendent and immanent God (theism). This truth has specific implications for the doctrine on providence inter alia. When Reformed dogmatics is practised in cooperation with other theological disciplines, philosophy, literature studies, et cetera, theology in the end becomes doxology.

scholarly journals s-Lecture hall partitions, self-reciprocal polynomials, and Gorenstein cones

2014 ◽  
Vol 36 (1-2) ◽  
pp. 123-147 ◽  
Author(s):  
Matthias Beck ◽  
Benjamin Braun ◽  
Matthias Köppe ◽  
Carla D. Savage ◽  
Zafeirakis Zafeirakopoulos
Keyword(s):  
Lecture Hall ◽  
Lecture Hall Partitions

scholarly journals The mathematics of lecture hall partitions

2016 ◽  
Vol 144 ◽  
pp. 443-475 ◽  
Author(s):  
Carla D. Savage
Keyword(s):  
Lecture Hall ◽  
Lecture Hall Partitions

scholarly journals Re-engaging Students by Teaching from the Middle and Back of a 500-seat Lecture Hall

2018 ◽  
Author(s):  
James Andrew Smith
Keyword(s):  
Content Delivery ◽  
Traditional Classroom ◽  
The Other ◽  
Lecture Hall ◽  
Classroom Teachers ◽  
Dynamic Content ◽  
The Future

Abstract – To better engage with students, especially in a large traditional classroom, one should consider teaching from multiple locations within the classroom, not just in the front. In classes where computers can be used to project material to the front of the classroom teachers should consider wireless peripherals or computers to achieve dynamic content delivery from beyond the podium. A variety of technologies were examined here, with wireless Wacom drawing tablets paired with either Apple or Windows computers, Miracast-enabled Windows tablets, and Doceri’s Whiteboard mode on Windows tablets and Apple iPads yielding the best results. The Wacom Tablet and Apple Trackpad were found to enable greater engagement of students, from the front to the rear of the classroom. More rigorous tests with the other technologies is to be carried out in the future.  

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 $R(w_0)$.

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