scholarly journals The alternating PBW basis for the positive part of Uq(sl^2)

2019 ◽  
Vol 60 (7) ◽  
pp. 071704
Author(s):  
Paul Terwilliger
Keyword(s):  
Positive Part ◽  
Pbw Basis

The positive-part Stein-rule estimator and tests of linear hypotheses

1988 ◽  
Vol 26 (1) ◽  
pp. 49-51 ◽  
Author(s):  
Aman Ullah ◽  
David E.A. Giles
Keyword(s):  
Positive Part ◽  
Tests Of Linear Hypotheses

scholarly journals Facets of the Generalized Cluster Complex and Regions in the Extended Catalan Arrangement of Type $A$

10.37236/3169 ◽  
2013 ◽  
Vol 20 (4) ◽  
Author(s):  
Susanna Fishel ◽  
Myrto Kallipoliti ◽  
Eleni Tzanaki
Keyword(s):  
Simple Root ◽  
Type A ◽  
Cluster Complex ◽  
Integer Partitions ◽  
Positive Part

In this paper we present a bijection between two well known families of Catalan objects: the set of facets of the $m$-generalized cluster complex $\Delta^m(A_n)$ and that of dominant regions in the $m$-Catalan arrangement ${\rm Cat}^m(A_n)$, where $m\in\mathbb{N}_{>0}$. In particular, the map which we define bijects facets containing the negative simple root $-\alpha$ to dominant regions having the hyperplane $\{v\in V\mid\left\langle v,\alpha \right\rangle=m\}$ as separating wall. As a result, it restricts to a bijection between the set of facets of the positive part of $\Delta^m(A_n)$ and the set of bounded dominant regions in ${\rm Cat}^m(A_n)$. Our map is a composition of two bijections in which integer partitions in an $m$-dilated $n$-staircase shape come into play.

Büchner, Friedrich Karl Christian Ludwig (Louis) (1824–99)

2018 ◽  
Author(s):  
Michael Heidelberger
Keyword(s):  
Nineteenth Century ◽  
Empirical Science ◽  
Human Beings ◽  
Positive Part

Ludwig Büchner wrote one of the most popular and polemical books of the strong materialist movement in later nineteenth century Germany, his Kraft und Stoff (Force and Matter) (1855). He tried to develop a comprehensive worldview, which was based solely on the findings of empirical science and did not take refuge in religion or any other transcendent categories in explaining nature and its development, including human beings. When Büchner tried to expose the backwardness of traditional philosophical and religious views in scientific matters, his arguments had some force, but the positive part of his programme was not free of superficiality and naivety. Büchner’s writings helped to strengthen progressive and rational traditions inside and outside philosophy, but they can also serve as the prime example of the uncritical nineteenth-century belief in science’s capacity to redeem humankind from all evil.

Generic Extensions and Canonical Bases for Cyclic Quivers

2007 ◽  
Vol 59 (6) ◽  
pp. 1260-1283 ◽  
Author(s):  
Bangming Deng ◽  
Jie Du ◽  
Jie Xiao
Keyword(s):  
Hall Algebra ◽  
Quiver Representations ◽  
Algebraic Construction ◽  
Positive Part ◽  
Monomial Basis ◽  
Canonical Bases ◽  
Generic Extensions ◽  
Cyclic Quiver

AbstractWe use the monomial basis theory developed by Deng and Du to present an elementary algebraic construction of the canonical bases for both the Ringel–Hall algebra of a cyclic quiver and the positive part U+of the quantum affine. This construction relies on analysis of quiver representations and the introduction of a new integral PBW–like basis for the Lusztig ℤ[v,v–1]-form of U+.

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