Reversible coagulation-fragmentation processes and random combinatorial structures: Asymptotics for the number of groups

2004 ◽  
Vol 25 (2) ◽  
pp. 227-245 ◽  
Author(s):  
Michael M. Erlihson ◽  
Boris L. Granovsky
Keyword(s):  
Combinatorial Structures ◽  
Reversible Coagulation ◽  
Fragmentation Processes

scholarly journals Asymptotic formula for a partition function of reversible coagulation-fragmentation processes

2002 ◽  
Vol 130 (1) ◽  
pp. 259-279 ◽  
Author(s):  
Gregory A. Freiman ◽  
Boris L. Granovsky
Keyword(s):  
Partition Function ◽  
Asymptotic Formula ◽  
Reversible Coagulation ◽  
Fragmentation Processes

scholarly journals Fragmentation Processes During Strombolian Explosions Revealed Using Particle Size Distribution Mapping

2020 ◽  
Vol 8 ◽  
Author(s):  
Livia Colo’ ◽  
Maurizio Ripepe ◽  
Lucia Gurioli ◽  
Andrew J. L. Harris
Keyword(s):  
Particle Size ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Distribution Mapping ◽  
Strombolian Explosions ◽  
Fragmentation Processes

The Transition Matrix Between the Specht and 𝔰𝔩3 Web Bases is Unitriangular With Respect to Shadow Containment

2020 ◽  
Author(s):  
Heather M Russell ◽  
Julianna Tymoczko
Keyword(s):  
Symmetric Group ◽  
Partial Order ◽  
Transition Matrix ◽  
Group Representation ◽  
Jones Polynomial ◽  
Basis Matrix ◽  
Combinatorial Structures ◽  
Quantum Invariants ◽  
One Dimensional ◽  
Link Diagrams

Abstract Webs are planar graphs with boundary that describe morphisms in a diagrammatic representation category for $\mathfrak{sl}_k$. They are studied extensively by knot theorists because braiding maps provide a categorical way to express link diagrams in terms of webs, producing quantum invariants like the well-known Jones polynomial. One important question in representation theory is to identify the relationships between different bases; coefficients in the change-of-basis matrix often describe combinatorial, algebraic, or geometric quantities (e.g., Kazhdan–Lusztig polynomials). By ”flattening” the braiding maps, webs can also be viewed as the basis elements of a symmetric group representation. In this paper, we define two new combinatorial structures for webs: band diagrams and their one-dimensional projections, shadows, which measure depths of regions inside the web. As an application, we resolve an open conjecture that the change of basis between the so-called Specht basis and web basis of this symmetric group representation is unitriangular for $\mathfrak{sl}_3$-webs ([ 33] and [ 29].) We do this using band diagrams and shadows to construct a new partial order on webs that is a refinement of the usual partial order. In fact, we prove that for $\mathfrak{sl}_2$-webs, our new partial order coincides with the tableau partial order on webs studied by the authors and others [ 12, 17, 29, 33]. We also prove that though the new partial order for $\mathfrak{sl}_3$-webs is a refinement of the previously studied tableau order, the two partial orders do not agree for $\mathfrak{sl}_3$.

scholarly journals Teaching Combinatorial Principles Using Relations through the Placemat Method

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1825
Author(s):  
Viliam Ďuriš ◽  
Gabriela Pavlovičová ◽  
Dalibor Gonda ◽  
Anna Tirpáková
Keyword(s):  
Graph Theory ◽  
Complexity Theory ◽  
Slovak Republic ◽  
Teaching Mathematics ◽  
Combinatorial Structures ◽  
Algorithmic Approach ◽  
Scientific Disciplines ◽  
Combinatorial Principles ◽  
The Subject ◽  
As Graph

The presented paper is devoted to an innovative way of teaching mathematics, specifically the subject combinatorics in high schools. This is because combinatorics is closely connected with the beginnings of informatics and several other scientific disciplines such as graph theory and complexity theory. It is important in solving many practical tasks that require the compilation of an object with certain properties, proves the existence or non-existence of some properties, or specifies the number of objects of certain properties. This paper examines the basic combinatorial structures and presents their use and learning using relations through the Placemat method in teaching process. The effectiveness of the presented innovative way of teaching combinatorics was also verified experimentally at a selected high school in the Slovak Republic. Our experiment has confirmed that teaching combinatorics through relationships among talented children in mathematics is more effective than teaching by a standard algorithmic approach.

scholarly journals Ash from the Eyjafjallajökull eruption (Iceland): Fragmentation processes and aerodynamic behavior

2012 ◽  
Vol 117 (B9) ◽  
Author(s):  
P. Dellino ◽  
M. T. Gudmundsson ◽  
G. Larsen ◽  
D. Mele ◽  
J. A. Stevenson ◽  
...  
Keyword(s):  
Fragmentation Processes

scholarly journals Study of Lie algebras by using combinatorial structures

2012 ◽  
Vol 436 (2) ◽  
pp. 349-363 ◽  
Author(s):  
Manuel Ceballos ◽  
Juan Núñez ◽  
Ángel F. Tenorio
Keyword(s):  
Lie Algebras ◽  
Combinatorial Structures
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