Bounded compositions and products of chains, or bi(s)nomials everywhere from de Moivre's formula to spin multiplicities and constant-sum codes
This paper unifies diverse mathematical interpretations of the coefficients of bounded chain products—ranging from de Moivre's dice problem and spin multiplicities to constant-sum codes—by establishing a common notation, proving symmetry and log-concavity properties, and deriving explicit asymptotic expansions and limit behaviors for both equal and arbitrary bounds.
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