Combinatorial Hopf algebra of superclass functions of type D

International audience We provide a Hopf algebra structure on the supercharacter theory for the unipotent upper triangular group of type {D} over a finite field. Also, we make further comments with respect to types {B} and {C}. Type {A} was explored by M. Aguiar et. al (2010), thus this extended abstract is a contribution to understand combinatorially the supercharacter theory of the other classical Lie types. Dotamos con una estructura de álgebra de Hopf la teoría de supercaracteres del grupo de matrices unipotentes triangulares superiores de tipo{D} sobre un cuerpo finito. Ademas, discutimos brevemente los tipos {B} y {C}. El tipo A fue explorado por M. Aguiar et al (2010), por lo tanto este resumen extendido es una contribución para entender combinatoriamente la teoría de supercaracteres de los otros tipos de Lie clásicos. Nous construisons une structure d'algèbre de Hopf sur la thérie des supercharactères du groupe de matrices unipotentes triangulaires supéieures de type {D}. Nous donnons aussi quelques commentaires à l'égard des types {B} et {C} . Le type {A} a été explorée par M. Aguiar et al. (2010), donc ce résumé étendu est une contribution à la théorie combinatoire des supercharactères pour les autres types de Lie classiques. \par

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Lattice of combinatorial Hopf algebras: binary trees with multiplicities

Discrete Mathematics & Theoretical Computer Science ◽

10.46298/dmtcs.2372 ◽

2013 ◽

Vol DMTCS Proceedings vol. AS,... (Proceedings) ◽

Author(s):

Jean-Baptiste Priez

Keyword(s):

Hopf Algebra ◽

Hopf Algebras ◽

Lattice Structure ◽

Binary Trees ◽

Hook Length ◽

Combinatorial Hopf Algebras ◽

Combinatorial Hopf Algebra ◽

International Audience ◽

Comme Application ◽

Premiere Partie

International audience In a first part, we formalize the construction of combinatorial Hopf algebras from plactic-like monoids using polynomial realizations. Thank to this construction we reveal a lattice structure on those combinatorial Hopf algebras. As an application, we construct a new combinatorial Hopf algebra on binary trees with multiplicities and use it to prove a hook length formula for those trees. Dans une première partie, nous formalisons la construction d’algèbres de Hopf combinatoires à partir d’une réalisation polynomiale et de monoïdes de type monoïde plaxique. Grâce à cette construction, nous mettons à jour une structure de treillis sur ces algèbres de Hopf combinatoires. Comme application, nous construisons une nouvelle algèbre de Hopf sur des arbres binaires à multiplicités et on l’utilise pour démontrer une formule des équerressur ces arbres.

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A polynomial realization of the Hopf algebra of uniform block permutations

Discrete Mathematics & Theoretical Computer Science ◽

10.46298/dmtcs.3031 ◽

2012 ◽

Vol DMTCS Proceedings vol. AR,... (Proceedings) ◽

Author(s):

Rémi Maurice

Keyword(s):

Hopf Algebra ◽

Poster Session ◽

Combinatorial Hopf Algebra ◽

Noncommutative Polynomials ◽

International Audience

Poster session International audience We investigate the combinatorial Hopf algebra based on uniform block permutations and we realize this algebra in terms of noncommutative polynomials in inﬁnitely many bi-letters.

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Integer points enumerator of hypergraphic polytopes

Publications de l Institut Mathematique ◽

10.2298/pim200205001p ◽

2021 ◽

pp. 1-1

Author(s):

Marko Pesovic

Keyword(s):

Positive Integer ◽

Hopf Algebra ◽

Symmetric Function ◽

Quasisymmetric Function ◽

Quasisymmetric Functions ◽

Simple Graphs ◽

Integer Points ◽

Combinatorial Hopf Algebra ◽

Chromatic Symmetric Function

For a hypergraphic polytope there is a weighted quasisymmetric function which enumerates positive integer points in its normal fan and determines its f-polynomial. This quasisymmetric function invariant of hypergraphs extends the Stanley chromatic symmetric function of simple graphs. We consider a certain combinatorial Hopf algebra of hypergraphs and show that universal morphism to quasisymmetric functions coincides with this enumerator function. We calculate the f-polynomial of uniform hypergraphic polytopes.

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The Type D Construct

European Journal of Psychological Assessment ◽

10.1027/1015-5759/a000189 ◽

2014 ◽

Vol 30 (4) ◽

pp. 283-288 ◽

Cited By ~ 3

Author(s):

Gesine Grande ◽

Matthias Romppel ◽

Matthias Michal ◽

Elmar Brähler

Keyword(s):

Social Functioning ◽

Negative Affectivity ◽

Population Based ◽

Type D Personality ◽

Social Orientation ◽

German Population ◽

Social Competencies ◽

Social And Emotional ◽

Type D ◽

Worse Prognosis

The interaction of negative affectivity (NA) and social inhibition (SI), known as the Type D personality, is associated with a worse prognosis in cardiac patients. Until now, causal models have been speculative, and this is partly due to a lack of clarity related to the validity of SI, its role in emotion regulation, and the postulated independence of social and emotional functioning. To examine the construct validity of the Type D personality, we analyzed associations of NA and SI with different measures of affectivity, social anxiety, and social competencies in a German population-based representative sample (n = 2,495). Both NA and SI were associated with all other measures of social functioning and negative affect (all rs > .30) and showed considerable cross-loadings (NA: a 1 = .39, a 2 = .63; SI: a1 = .73 and a2 = .34) in a two-factor solution with the factors labeled as Social Functioning and Negative Affectivity. The SI subscale did not properly differentiate between social fears and social competencies, which emerged as rather different aspects of social functioning. Further studies should examine the effect of broader dimensions of social orientation and competencies and their interaction with NA on cardiac prognosis.

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Illness Perception and Its Changes During Six Months After Cardiac Rehabilitation

European Journal of Health Psychology ◽

10.1027/2512-8442/a000034 ◽

2019 ◽

Vol 26 (3) ◽

pp. 90-100

Author(s):

Justė Lukoševičiūtė ◽

Kastytis Šmigelskas

Keyword(s):

New York ◽

Social Factors ◽

Nyha Class ◽

Illness Perception ◽

Heart Association ◽

Class Iii ◽

Cognitive Representations ◽

Coronary Syndrome ◽

Type D ◽

New York Heart Association

Abstract. Illness perception is a concept that reflects patients' emotional and cognitive representations of disease. This study assessed the illness perception change during 6 months in 195 patients (33% women and 67% men) with acute coronary syndrome, taking into account the biological, psychological, and social factors. At baseline, more threatening illness perception was observed in women, persons aged 65 years or more, with poorer functional capacity (New York Heart Association [NYHA] class III or IV) and comorbidities ( p < .05). Type D personality was the only independent factor related to more threatening illness perception (βs = 0.207, p = .006). At follow-up it was found that only self-reported cardiovascular impairment plays the role in illness perception change (βs = 0.544, p < .001): patients without impairment reported decreasing threats of illness, while the ones with it had a similar perception of threat like at baseline. Other biological, psychological, and social factors were partly associated with illness perception after an acute cardiac event but not with perception change after 6 months.

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