scholarly journals Root Cones and the Resonance Arrangement

10.37236/8759 ◽  
2021 ◽  
Vol 28 (1) ◽  
Author(s):  
Samuel C. Gutekunst ◽  
Karola Mészáros ◽  
T. Kyle Petersen
Keyword(s):  
Partition Function ◽  
Data Structures ◽  
Hyperplane Arrangement ◽  
Type A ◽  
Dimensional Case ◽  
Threshold Functions ◽  
Kostant Partition Function ◽  
Root Polytope ◽  
The Way

We study the connection between triangulations of a type $A$ root polytope and the resonance arrangement, a hyperplane arrangement that shows up in a surprising number of contexts. Despite an elementary definition for the resonance arrangement, the number of resonance chambers has only been computed up to the $n=8$ dimensional case. We focus on data structures for labeling chambers, such as sign vectors and sets of alternating trees, with an aim at better understanding the structure of the resonance arrangement, and, in particular, enumerating its chambers. Along the way, we make connections with similar (and similarly difficult) enumeration questions. With the root polytope viewpoint, we relate resonance chambers to the chambers of polynomiality of the Kostant partition function. With the hyperplane viewpoint, we clarify the connections between resonance chambers and threshold functions. In particular, we show that the base-2 logarithm of the number of resonance chambers is asymptotically $n^2$.

LANDAU-GINZBURG TOPOLOGICAL THEORIES IN THE FRAMEWORK OF GKM AND EQUIVALENT HIERARCHIES

1993 ◽  
Vol 08 (11) ◽  
pp. 1047-1061 ◽  
Author(s):  
S. KHARCHEV ◽  
A. MARSHAKOV ◽  
A. MIRONOV ◽  
A. MOROZOV
Keyword(s):  
Partition Function ◽  
Point Of View ◽  
General Context ◽  
Integrable Structure ◽  
Integrable Theory ◽  
String Models ◽  
Topological Theories ◽  
The Way

We consider the deformations of "monomial solutions" to generalized Kontsevich. model1,2 and establish the relation between the flows generated by these deformations with those of N = 2 Landau-Ginzburg topological theories. We prove that the partition function of a generic generalized Kontsevich model can be presented as a product of some "quasiclassical" factor and non-deformed partition function which depends only on the sum of Miwa transformed and flat times. This result is important for the restoration of explicit p − q symmetry in the interpolation pattern between all the (p, q)-minimal string models with c < 1 and for revealing its integrable structure in p-direction, determined by deformations of the potential. It also implies the way in which supersymmetric LandauGinzburg models are embedded into the general context of GKM. From the point of view of integrable theory these deformations present a particular case of what is called equivalent hierarchies.

The contrast between interrogatives and questions

1994 ◽  
Vol 30 (2) ◽  
pp. 411-439 ◽  
Author(s):  
Rodney Huddleston
Keyword(s):  
Sentence Type ◽  
Type A ◽  
Grammatical Form ◽  
The Way

This paper explores the relation between interrogative, a category of grammatical form, and question, a category of meaning. Interrogative contrasts with declarative, imperative, etc., in the system of clause type (not sentence type); a question defines a set of answers. Two kinds of interrogative are distinguished, closed and open -though in some languages they may be distinct primary classes. Three kinds of question are distinguished according to the way the set of answers is defined: polar, alternative and variable questions; another dimension distinguishes information from direction questions. Mismatches between interrogatives and questions are found in the areas of coordination, parentheticals, echoes and questions signalled only prosodically. Mismatches between interrogative phrases and questioned elements are also investigated.

scholarly journals Face monoid actions and tropical hyperplane arrangements

2017 ◽  
Vol 27 (08) ◽  
pp. 1001-1025
Author(s):  
Marianne Johnson ◽  
Mark Kambites
Keyword(s):  
Hyperplane Arrangement ◽  
Hyperplane Arrangements ◽  
Oriented Matroid ◽  
Definition Of ◽  
The Way

We study the combinatorics of tropical hyperplane arrangements, and their relationship to (classical) hyperplane face monoids. We show that the refinement operation on the faces of a tropical hyperplane arrangement, introduced by Ardila and Develin in their definition of a tropical oriented matroid, induces an action of the hyperplane face monoid of the classical braid arrangement on the arrangement, and hence on a number of interesting related structures. Along the way, we introduce a new characterization of the types (in the sense of Develin and Sturmfels) of points with respect to a tropical hyperplane arrangement, in terms of partial bijections which attain permanents of submatrices of a matrix which naturally encodes the arrangement.

The social desirability of the Type A behaviour pattern

1986 ◽  
Vol 16 (4) ◽  
pp. 805-811 ◽  
Author(s):  
Adrian Furnham
Keyword(s):  
Social Desirability ◽  
Type A ◽  
Behaviour Pattern ◽  
Type B ◽  
Lower Type ◽  
Psychological Phenomena ◽  
The Social ◽  
Fake Good ◽  
Positive Light ◽  
The Way

SynopsisNearly one hundred subjects completed two Type A behaviour questionnaires twice. First, they were asked to complete them honestly, reporting accurately on their behaviour patterns. Half of the subjects were then asked to fake good, presenting themselves in a positive light, and half to fake bad, presenting themselves in a negative light. There was only a marginal difference on one questionnaire's total score, with fake good subjects having lower Type A (i.e. higher Type B scores) yet nearly every individual question revealed large significant differences. The subjects' own A/B classification did not effect the way in which they faked the questionnaires. The results are discussed in terms of the literature on faking, lay concepts of psychological phenomena and the multidimensionality of the Type A concept.

scholarly journals Topological flatness of local models for ramified unitary groups. II. The even dimensional case

2013 ◽  
Vol 13 (2) ◽  
pp. 303-393 ◽  
Author(s):  
Brian D. Smithling
Keyword(s):  
Local Structure ◽  
Unitary Groups ◽  
Dimensional Case ◽  
Shimura Varieties ◽  
Local Models ◽  
Admissible Set ◽  
The Way ◽  
Moduli Problems

AbstractLocal models are schemes, defined in terms of linear-algebraic moduli problems, which are used to model the étale-local structure of integral models of certain$p$-adic PEL Shimura varieties defined by Rapoport and Zink. In the case of a unitary similitude group whose localization at${ \mathbb{Q} }_{p} $is ramified, quasi-split$G{U}_{n} $, Pappas has observed that the original local models are typically not flat, and he and Rapoport have introduced new conditions to the original moduli problem which they conjecture to yield a flat scheme. In a previous paper, we proved that their new local models are topologically flat when$n$is odd. In the present paper, we prove topological flatness when$n$is even. Along the way, we characterize the$\mu $-admissible set for certain cocharacters$\mu $in types$B$and$D$, and we show that for these cocharacters admissibility can be characterized in a vertexwise way, confirming a conjecture of Pappas and Rapoport.

scholarly journals The Link Between Personal Factors and Workaholism: The Role of Remote Working During the COVID-19 Pandemic

Psichologija ◽  
2021 ◽  
Vol 64 ◽  
pp. 12-22
Author(s):  
Modesta Morkevičiūtė ◽  
Auksė Endriulaitienė
Keyword(s):  
Type A ◽  
Well Being ◽  
Important Variable ◽  
Remote Work ◽  
Personal Factors ◽  
Remote Workers ◽  
Type A Personality ◽  
The Relationship ◽  
The Way

The aim of the present study was to investigate the role of the way of doing work for the relationship between employees’ perfectionism, type A personality and workaholism during COVID-19 pandemic. A total of 668 Lithuanian employees participated in a study. The sample included employees who worked in the workplace (n = 331), as well as those who worked completely from home (n = 337). The levels of workaholism were measured using DUWAS-10 (Schaufeli et al., 2009). A multidimensional perfectionism scale (Hewitt et al., 1991) was used for the measurement of perfectionism. Type A personality was assessed with the help of the Framingham type A personality scale (Haynes et al., 1980). It was revealed in a study that the positive relationship between perfectionism and workaholism was stronger in the group of complete remote workers. It was further found that the moderating role of the way of doing work was not significant for the relationship between type A personality and workaholism. Overall, the findings support the idea that remote work is an important variable determining the development of health-damaging working behaviors among those employees who excel perfectionistic attributes. Therefore, the way of doing work must be considered when addressing the well-being of employees.

scholarly journals The polytope of Tesler matrices

2015 ◽  
Vol DMTCS Proceedings, 27th... (Proceedings) ◽  
Author(s):  
Karola Mészáros ◽  
Alejandro H. Morales ◽  
Brendon Rhoades
Keyword(s):  
Partition Function ◽  
Catalan Numbers ◽  
Young Tableaux ◽  
Integer Points ◽  
International Audience ◽  
Kostant Partition Function ◽  
Tesler Matrices ◽  
Flow Polytope ◽  
Standard Young Tableaux

26 pages, 4 figures. v2 has typos fixed, updated references, and a final remarks section including remarks from previous sections International audience We introduce the Tesler polytope $Tes_n(a)$, whose integer points are the Tesler matrices of size n with hook sums $a_1,a_2,...,a_n in Z_{\geq 0}$. We show that $Tes_n(a)$ is a flow polytope and therefore the number of Tesler matrices is counted by the type $A_n$ Kostant partition function evaluated at $(a_1,a_2,...,a_n,-\sum_{i=1}^n a_i)$. We describe the faces of this polytope in terms of "Tesler tableaux" and characterize when the polytope is simple. We prove that the h-vector of $Tes_n(a)$ when all $a_i>0$ is given by the Mahonian numbers and calculate the volume of $Tes_n(1,1,...,1)$ to be a product of consecutive Catalan numbers multiplied by the number of standard Young tableaux of staircase shape. On présente le polytope de Tesler $Tes_n(a)$, dont les points réticuilaires sont les matrices de Tesler de taillen avec des sommes des équerres $a_1,a_2,...,a_n in Z_{\geq 0}$. On montre que $Tes_n(a)$ est un polytope de flux. Donc lenombre de matrices de Tesler est donné par la fonction de Kostant de type An évaluée à ($(a_1,a_2,...,a_n,-\sum_{i=1}^n a_i)$On décrit les faces de ce polytope en termes de “tableaux de Tesler” et on caractérise quand le polytope est simple.On montre que l’h-vecteur de $Tes_n(a)$ , quand tous les $a_i>0$ , est donnée par le nombre de permutations avec unnombre donné d’inversions et on calcule le volume de T$Tes_n(1,1,...,1)$ comme un produit de nombres de Catalanconsécutives multiplié par le nombre de tableaux standard de Young en forme d’escalier

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