On the Combinatorial Representation of Information

2006 ◽  
pp. 479-488 ◽  
Author(s):  
Joel Ratsaby
Keyword(s):  
Combinatorial Representation

scholarly journals Combinatorial Expansions in $K$-Theoretic Bases

10.37236/2320 ◽  
2012 ◽  
Vol 19 (4) ◽  
Author(s):  
Jason Bandlow ◽  
Jennifer Morse
Keyword(s):  
Generating Functions ◽  
Symmetric Functions ◽  
Schur Functions ◽  
Geometric Information ◽  
Combinatorial Description ◽  
Littlewood Polynomials ◽  
Stanley Symmetric Functions ◽  
K Theory ◽  
Combinatorial Representation

We study the class $\mathcal C$ of symmetric functions whose coefficients in the Schur basis can be described by generating functions for sets of tableaux with fixed shape.  Included in this class are the Hall-Littlewood polynomials, $k$-Schur functions, and Stanley symmetric functions; functions whose Schur coefficients encode combinatorial, representation theoretic and geometric information. While Schur functions represent the cohomology of the Grassmannian variety of $GL_n$, Grothendieck functions $\{G_\lambda\}$ represent the $K$-theory of the same space.  In this paper, we give a combinatorial description of the coefficients when any element of $\mathcal C$ is expanded in the $G$-basis or the basis dual to $\{G_\lambda\}$.

COMBINATORIAL APPROACH TO COMPUTING COMPONENT IMPORTANCE INDEXES IN COHERENT SYSTEMS

2011 ◽  
Vol 26 (1) ◽  
pp. 117-128 ◽  
Author(s):  
Ilya B. Gertsbakh ◽  
Yoseph Shpungin
Keyword(s):  
System Reliability ◽  
Simple Formula ◽  
Analytic Formula ◽  
Importance Measure ◽  
Coherent Systems ◽  
Joint Reliability ◽  
Component Importance ◽  
Definition Of ◽  
Combinatorial Parameter ◽  
Combinatorial Representation

We consider binary coherent systems with independent binary components having equal failure probability q. The system DOWN probability is expressed via its signature's combinatorial analogue, the so-called D-spectrum. Using the definition of the Birnbaum importance measure (BIM), we introduce for each component a new combinatorial parameter, so-called BIM-spectrum, and develop a simple formula expressing component BIM via the component BIM-spectrum. Further extension of this approach allows obtaining a combinatorial representation for the joint reliability importance (JRI) of two components. To estimate component BIMs and JRIs, there is no need to know the analytic formula for system reliability. We demonstrate how our method works using the Monte Carlo approach. We present several examples of estimating component importance measures in a network when the DOWN state is defined as the loss of terminal connectivity.

Combinatorial representation of invariants of a soliton cellular automaton

1996 ◽  
Vol 92 (3-4) ◽  
pp. 209-220 ◽  
Author(s):  
Makoto Torii ◽  
Daisuke Takahashi ◽  
Junkichi Satsuma
Keyword(s):  
Cellular Automaton ◽  
Combinatorial Representation

scholarly journals Combinatorial Representation Theory

2010 ◽  
pp. 799-882
Author(s):  
Christine Bessenrodt ◽  
Francesco Brenti ◽  
Alexander Kleshchev ◽  
Arun Ram
Keyword(s):  
Representation Theory ◽  
Combinatorial Representation Theory ◽  
Combinatorial Representation

scholarly journals Combinatorial Representation of Parameter Space for Switching Networks

2016 ◽  
Vol 15 (4) ◽  
pp. 2176-2212 ◽  
Author(s):  
Bree Cummins ◽  
Tomas Gedeon ◽  
Shaun Harker ◽  
Konstantin Mischaikow ◽  
Kafung Mok
Keyword(s):  
Parameter Space ◽  
Switching Networks ◽  
Combinatorial Representation

Feature extraction and combinatorial representation of neuronal input pattern by Ca2+ signaling pathways

2011 ◽  
Vol 71 ◽  
pp. e116
Author(s):  
Hajime Fujii ◽  
Masatoshi Inoue ◽  
Hiroyuki Okuno ◽  
Sayaka Takemoto-Kimura ◽  
Haruhiko Bito
Keyword(s):  
Feature Extraction ◽  
Signaling Pathways ◽  
Input Pattern ◽  
Combinatorial Representation

scholarly journals The categorified Heisenberg algebra I: A combinatorial representation

2018 ◽  
Vol 222 (3) ◽  
pp. 703-745
Author(s):  
Jeffrey C. Morton ◽  
Jamie Vicary
Keyword(s):  
Algebra I ◽  
Heisenberg Algebra ◽  
Combinatorial Representation
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