scholarly journals A Bijection for Tricellular Maps

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Hillary S. W. Han ◽  
Christian M. Reidys
Keyword(s):  
Matrix Theory ◽  
Dyson Equation ◽  
Cutting Edge ◽  
Edge Deletion ◽  
Cell Complexes ◽  
Bijective Proof ◽  
Edge Contraction ◽  
Orientable Surfaces

We give a bijective proof for a relation between unicellular, bicellular, and tricellular maps. These maps represent cell complexes of orientable surfaces having one, two, or three boundary components. The relation can formally be obtained using matrix theory (Dyson, 1949) employing the Schwinger-Dyson equation (Schwinger, 1951). In this paper we present a bijective proof of the corresponding coefficient equation. Our result is a bijection that transforms a unicellular map of genus g into unicellular, bicellular or tricellular maps of strictly lower genera. The bijection employs edge cutting, edge contraction, and edge deletion.

scholarly journals Posets from Admissible Coxeter Sequences

10.37236/684 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Matthew Macauley ◽  
Henning S. Mortveit
Keyword(s):  
Coxeter Groups ◽  
Conjugacy Problem ◽  
Equivalence Classes ◽  
Quiver Representations ◽  
Edge Deletion ◽  
Acyclic Orientations ◽  
Edge Contraction ◽  
Combinatorial Invariant ◽  
Source To Sink ◽  
Admissible Sequences

We study the equivalence relation on the set of acyclic orientations of an undirected graph $\Gamma$ generated by source-to-sink conversions. These conversions arise in the contexts of admissible sequences in Coxeter theory, quiver representations, and asynchronous graph dynamical systems. To each equivalence class we associate a poset, characterize combinatorial properties of these posets, and in turn, the admissible sequences. This allows us to construct an explicit bijection from the equivalence classes over $\Gamma$ to those over $\Gamma'$ and $\Gamma"$, the graphs obtained from $\Gamma$ by edge deletion and edge contraction of a fixed cycle-edge, respectively. This bijection yields quick and elegant proofs of two non-trivial results: $(i)$ A complete combinatorial invariant of the equivalence classes, and $(ii)$ a solution to the conjugacy problem of Coxeter elements for simply-laced Coxeter groups. The latter was recently proven by H. Eriksson and K. Eriksson using a much different approach.

scholarly journals Cutting Edge: Deletion of Ezrin in B Cells of Lyn-Deficient Mice Downregulates Lupus Pathology

2018 ◽  
Vol 201 (5) ◽  
pp. 1353-1358 ◽  
Author(s):  
Debasis Pore ◽  
Emily Huang ◽  
Dina Dejanovic ◽  
Neetha Parameswaran ◽  
Michael B. Cheung ◽  
...  
Keyword(s):  
B Cells ◽  
Cutting Edge ◽  
Edge Deletion ◽  
Deficient Mice

scholarly journals Matrix theory on non-orientable surfaces

1998 ◽  
Vol 429 (1-2) ◽  
pp. 27-34 ◽  
Author(s):  
Gysbert Zwart
Keyword(s):  
Matrix Theory ◽  
Orientable Surfaces

scholarly journals On the removal of forbidden graphs by edge-deletion or by edge-contraction

1981 ◽  
Vol 3 (2) ◽  
pp. 151-153 ◽  
Author(s):  
Toshimasa Watanabe ◽  
Tadashi Ae ◽  
Akira Nakamura
Keyword(s):  
Edge Deletion ◽  
Edge Contraction

Plastic Deformation in Microtomed Sections

1971 ◽  
Vol 29 ◽  
pp. 458-459
Author(s):  
J. Temple Black
Keyword(s):  
Plastic Deformation ◽  
Plastic Strain ◽  
Applied Stress ◽  
Elastic Strain ◽  
High Strain ◽  
Tool Material ◽  
Cutting Edge ◽  
Material Structure ◽  
Geometrical Constraints

The output of the ultramicrotomy process with its high strain levels is dependent upon the input, ie., the nature of the material being machined. Apart from the geometrical constraints offered by the rake and clearance faces of the tool, each material is free to deform in whatever manner necessary to satisfy its material structure and interatomic constraints. Noncrystalline materials appear to survive the process undamaged when observed in the TEM. As has been demonstrated however microtomed plastics do in fact suffer damage to the top and bottom surfaces of the section regardless of the sharpness of the cutting edge or the tool material. The energy required to seperate the section from the block is not easily propogated through the section because the material is amorphous in nature and has no preferred crystalline planes upon which defects can move large distances to relieve the applied stress. Thus, the cutting stresses are supported elastically in the internal or bulk and plastically in the surfaces. The elastic strain can be recovered while the plastic strain is not reversible and will remain in the section after cutting is complete.

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