Root system graphs

(0,2)-graphs and root systems

We construct (0,2)-graphs from root systems with simply laced diagram and study their properties.

The Square Root Phenomenon in Planar Graphs

CRYSTAL GRAPHS AND q-ANALOGUES OF WEIGHT MULTIPLICITIES FOR THE ROOT SYSTEM

We give an expression of the q-analogues of the multiplicities of weights in irreducible sl n+1-modules in terms of the geometry of the crystal graph attached to the corresponding Uq(sl n+1)-modules. As an application, we describe multivariate polynomial analogues of the multiplicities of the zero weight, refining Kostant’s generalized exponents.

Kostka-Foulkes Polynomials Cyclage Graphs and Charge Statistic for the Root System Cn

We establish a Morris type recurrence formula for the root system Cn . Next we introduce cyclage graphs for the corresponding Kashiwara-Nakashima’s tableaux and use them to define a charge statistic. Finally we conjecture that this charge may be used to compute the Kostka-Foulkes polynomials for type Cn .

Alarm Root Cause Detection System

Production process control becomes complicated as the complexity of the controlled process grows. To simp113 the operator's role many computer based control systems with integrated visualization clients have been developed. In many practical circumstances malfunction of one or more process components results in other related components entering the alarm states. Several alarms appear on the ope...