scholarly journals Tamari lattices and noncrossing partitions in type B

2006 ◽  
Vol 306 (21) ◽  
pp. 2711-2723 ◽  
Author(s):  
Hugh Thomas
Keyword(s):  
Type B ◽  
Noncrossing Partitions ◽  
Tamari Lattices

scholarly journals Identities Derived from Noncrossing Partitions of Type $B$

10.37236/616 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
William Y. C. Chen ◽  
Andrew Y. Z. Wang ◽  
Alina F. Y. Zhao
Keyword(s):  
Type B ◽  
Noncrossing Partitions ◽  
Narayana Numbers ◽  
Combinatorial Constructions

Based on weighted noncrossing partitions of type $B$, we obtain type $B$ analogues of Coker's identities on the Narayana polynomials. A parity reversing involution is given for the alternating sum of Narayana numbers of type $B$. Moreover, we find type $B$ analogues of the refinements of Coker's identities due to Chen, Deutsch and Elizalde. By combinatorial constructions, we provide type $B$ analogues of three identities of Mansour and Sun also on the Narayana polynomials.

scholarly journals Parking Functions of Types A and B

10.37236/1668 ◽  
2001 ◽  
Vol 9 (1) ◽  
Author(s):  
P. Biane
Keyword(s):  
Symmetric Group ◽  
Cayley Graph ◽  
Parking Functions ◽  
Type B ◽  
Noncrossing Partitions ◽  
Edge Labeling

The lattice of noncrossing partitions can be embedded into the Cayley graph of the symmetric group. This allows us to rederive connections between noncrossing partitions and parking functions. We use an analogous embedding for type B non-crossing partitions in order to answer a question raised by R. Stanley on the edge labeling of the type B non-crossing partitions lattice.

scholarly journals Noncrossing Arc Diagrams, Tamari Lattices, and Parabolic Quotients of the Symmetric Group

2021 ◽  
Author(s):  
Henri Mühle
Keyword(s):  
Symmetric Group ◽  
Partial Order ◽  
Structural Investigation ◽  
Canonical Representation ◽  
Weak Order ◽  
Noncrossing Partitions ◽  
Tamari Lattice ◽  
Semidistributive Lattice ◽  
Tamari Lattices

AbstractOrdering permutations by containment of inversion sets yields a fascinating partial order on the symmetric group: the weak order. This partial order is, among other things, a semidistributive lattice. As a consequence, every permutation has a canonical representation as a join of other permutations. Combinatorially, these canonical join representations can be modeled in terms of arc diagrams. Moreover, these arc diagrams also serve as a model to understand quotient lattices of the weak order. A particularly well-behaved quotient lattice of the weak order is the well-known Tamari lattice, which appears in many seemingly unrelated areas of mathematics. The arc diagrams representing the members of the Tamari lattices are better known as noncrossing partitions. Recently, the Tamari lattices were generalized to parabolic quotients of the symmetric group. In this article, we undertake a structural investigation of these parabolic Tamari lattices, and explain how modified arc diagrams aid the understanding of these lattices.

scholarly journals Minimal transitive factorizations of a permutation of type (p,q)

2012 ◽  
Vol DMTCS Proceedings vol. AR,... (Proceedings) ◽  
Author(s):  
Jang Soo Kim ◽  
Seunghyun Seo ◽  
Heesung Shin
Keyword(s):  
Recent Result ◽  
Combinatorial Proof ◽  
Type B ◽  
Noncrossing Partitions ◽  
International Audience ◽  
Maximal Chains ◽  
Nous Utilisons

International audience We give a combinatorial proof of Goulden and Jackson's formula for the number of minimal transitive factorizations of a permutation when the permutation has two cycles. We use the recent result of Goulden, Nica, and Oancea on the number of maximal chains of annular noncrossing partitions of type B. Nous donnons une preuve combinatoire de formule de Goulden et Jackson pour le nombre de factorisations transitives minimales d'une permutation lorsque la permutation a deux cycles. Nous utilisons le rèsultat rècent de Goulden, Nica, et Oancea sur le nombre de chaî nes maximales des partitions non-croisèes annulaires de type B.

scholarly journals Combinatorial statistics on type-B analogues of noncrossing partitions and restricted permutations

10.37236/1487 ◽  
2000 ◽  
Vol 7 (1) ◽  
Author(s):  
Rodica Simion
Keyword(s):  
Type B ◽  
Noncrossing Partitions ◽  
Hyperoctahedral Group ◽  
Restricted Permutations ◽  
Symmetry Properties

We define type-B analogues of combinatorial statistics previously studied on noncrossing partitions and show that analogous equidistribution and symmetry properties hold in the case of type-B noncrossing partitions. We also identify pattern-avoiding classes of elements in the hyperoctahedral group which parallel known classes of restricted permutations with respect to their relations to noncrossing partitions.

Biological and Morphological Studies on Low-Leukemia-Strain Mice with Hodgkin's-Like Neoplasia Induced by Serial Cell-Free Transmission of Leukemic Organs of SJL/J Strain Mice

1968 ◽  
Vol 26 ◽  
pp. 210-211
Author(s):  
S. Fujinaga ◽  
K. Maruyama ◽  
C.W. Williams ◽  
K. Sekhri ◽  
L. Dmochowski
Keyword(s):  
Tissue Culture ◽  
Type A ◽  
Reticulum Cell ◽  
Type B ◽  
Viral Origin ◽  
Serial Transfer ◽  
Strain Mouse ◽  
Morphological Studies ◽  
Cell Neoplasm ◽  
Free Material

Yumoto and Dmochowski (Cancer Res.27, 2098 (1967)) reported the presence of mature and immature type C leukemia virus particles in leukemic organs and tissues such as lymph nodes, spleen, thymus, liver, and kidneys of SJL/J strain mice with Hodgki's-like disease or reticulum cell neoplasm (type B). In an attempt to ascertain the possibility that this neoplasia may be of viral origin, experiments with induction and transmission of this neoplasm were carried out using cell-free extracts of leukemic organs from an SJL/J strain mouse with spontaneous disease.It has been possible to induce the disease in low-leukemia BALB/c and C3HZB strain mice and serially transfer the neoplasia by cell-free extracts of leukemic organs of these mice. Histological examination revealed the neoplasia to be of either reticulum cell-type A or type B. Serial transfer is now in its fifth passage. In addition leukemic spleen from another SJL/J strain mouse with spontaneous reticulum cell neoplasm (type A) was set up in tissue culture and is now in its 141st serial passage in vitro. Preliminary results indicate that cell-free material of 39th tissue culture passage can reproduce neoplasia in BALB/c mice.

Cryo-electron microscopy of two-dimensional crystals of reduced type B botulinum neurotoxin

1992 ◽  
Vol 50 (1) ◽  
pp. 530-531
Author(s):  
P. F. Flicker ◽  
V.S. Kulkarni ◽  
J. P. Robinson ◽  
G. Stubbs ◽  
B. R. DasGupta
Keyword(s):  
Disulfide Bonds ◽  
Clostridium Botulinum ◽  
Structural Changes ◽  
Two Dimensional ◽  
Type B ◽  
Single Chain ◽  
Muscle Paralysis ◽  
Cryo Electron Microscopy ◽  
Disulfide Linkages ◽  
Intracellular Action

Botulinum toxin is a potent neurotoxin produced by Clostridium botulinum. The toxin inhibits release of neurotransmitter, causing muscle paralysis. There are several serotypes, A to G, all of molecular weight about 150,000. The protein exists as a single chain or or as two chains, with two disulfide linkages. In a recent investigation on intracellular action of neurotoxins it was reported that type B neurotoxin can inhibit the release of Ca++-activated [3H] norepinephrine only if the disulfide bonds are reduced. In order to investigate possible structural changes in the toxin upon reduction of the disulfide bonds, we have prepared two-dimensional crystals of reduced type B neurotoxin. These two-dimensional crystals will be compared with those of the native (unreduced) type B toxin.

Abstract #108: A Case of Type B Insulin Resistance

2004 ◽  
Vol 10 ◽  
pp. 37-38
Author(s):  
Lisa C. Moore ◽  
Archana Sadhu ◽  
Dorothy Martinez ◽  
Robin Kate Kelley
Keyword(s):  
Insulin Resistance ◽  
Type B
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