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.

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 Theta-Vexillary Signed Permutations

10.37236/8023 ◽  
2018 ◽  
Vol 25 (4) ◽  
Author(s):  
Jordan Lambert
Keyword(s):  
Pattern Avoidance ◽  
Type B ◽  
Hyperoctahedral Group ◽  
Degeneracy Loci ◽  
Signed Permutations

Theta-vexillary signed permutations are elements in the hyperoctahedral group that index certain classes of degeneracy loci of type B and C. These permutations are described using triples of $s$-tuples of integers subject to specific conditions. The objective of this work is to present different characterizations of theta-vexillary signed permutations, describing them in terms of corners in the Rothe diagram and pattern avoidance.

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.

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.

Semi-automated methods for 3-D reconstruction of macromolecular complexes

1995 ◽  
Vol 53 ◽  
pp. 42-43
Author(s):  
B. Carragher ◽  
M. Whittaker
Keyword(s):  
Three Dimensional ◽  
Time Saving ◽  
Macromolecular Complexes ◽  
Symmetry Properties ◽  
Dimensional Reconstruction ◽  
Experienced Operator ◽  
Projection Images ◽  
The Individual ◽  
Natural Symmetry

Techniques for three-dimensional reconstruction of macromolecular complexes from electron micrographs have been successfully used for many years. These include methods which take advantage of the natural symmetry properties of the structure (for example helical or icosahedral) as well as those that use single axis or other tilting geometries to reconstruct from a set of projection images. These techniques have traditionally relied on a very experienced operator to manually perform the often numerous and time consuming steps required to obtain the final reconstruction. While the guidance and oversight of an experienced and critical operator will always be an essential component of these techniques, recent advances in computer technology, microprocessor controlled microscopes and the availability of high quality CCD cameras have provided the means to automate many of the individual steps.During the acquisition of data automation provides benefits not only in terms of convenience and time saving but also in circumstances where manual procedures limit the quality of the final reconstruction.

Symmetry properties of a universal interaction

Physica ◽  
1952 ◽  
Vol 18 (2) ◽  
pp. 1017-1019 ◽  
Author(s):  
D PURSEY
Keyword(s):  
Symmetry Properties ◽  
Universal Interaction
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