Noncritical Resonances
Noncritical Resonances
This chapter deals with noncritical resonances. A short pattern is resonant at i if lsubscript i plus 1 = bᵢ. This property depends only on the associated prototype, so resonance is actually a property of prototypes. A first (middle) row entry is also called aᵢ critical if it is equal to one of its four neighbors, which are lᵢ, lsubscript i plus 1, bᵢ, and bsubscript i minus 1. We say that the resonance at i is critical if either aᵢ or asubscript i plus 1 is critical. The chapter introduces the relevant theorem, stating that if t is a strict pattern with no critical resonances, then t′ is also strict with no critical resonances. It also chooses a pair of canonical indexings of Γ = Γₜ and Δ′ = Δsubscript tprime.
Keywords: noncritical resonance, prototype, critical resonance, canonical indexings, short pattern
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