Conjecture expressing asymptotic growth of indecomposable summands in monoid-representation tensor powers via the Brauer character table of the group of units, with a proof under an extra hypothesis plus exact and asymptotic length formulas in good characteristic.
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Derives asymptotic formulas for the growth rate of the number of summands in tensor powers of the generating object in semisimple diagram/interpolation categories.
Formulas are discussed for the asymptotic growth rate of summands in tensor powers in monoidal categories with infinitely many indecomposables, using generalized Perron-Frobenius theory and random walk techniques.
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Growth Problems for Representations of Finite Monoids
Conjecture expressing asymptotic growth of indecomposable summands in monoid-representation tensor powers via the Brauer character table of the group of units, with a proof under an extra hypothesis plus exact and asymptotic length formulas in good characteristic.
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Growth problems in diagram categories
Derives asymptotic formulas for the growth rate of the number of summands in tensor powers of the generating object in semisimple diagram/interpolation categories.
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Asymptotics in infinite monoidal categories
Formulas are discussed for the asymptotic growth rate of summands in tensor powers in monoidal categories with infinitely many indecomposables, using generalized Perron-Frobenius theory and random walk techniques.