We characterize the permutative automorphisms of the Cuntz algebra On (namely, stable permutations) in terms of two sequences of graphs that we associate to any permutation of a discrete hypercube [n]t. As applications we show that in the limit of large t (resp. n) almost all permutations are not stable, thus proving Conj. 12.5 of Brenti and Conti [Adv. Math. 381 (2021), p. 60], characterize (and enumerate) stable quadratic 4 and 5-cycles, as well as a notable class of stable quadratic r-cycles, i.e. those admitting a compatible cyclic factorization by stable transpositions. Some of our results use new combinatorial concepts that may be of independent interest.

CUNTZ ALGEBRA AUTOMORPHISMS: GRAPHS AND STABILITY OF PERMUTATIONS / Brenti, F.; Conti, R.; Nenashev, G.. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - 377:12(2024), pp. 8433-8476. [10.1090/tran/9159]

CUNTZ ALGEBRA AUTOMORPHISMS: GRAPHS AND STABILITY OF PERMUTATIONS

Conti R.;Nenashev G.
2024

Abstract

We characterize the permutative automorphisms of the Cuntz algebra On (namely, stable permutations) in terms of two sequences of graphs that we associate to any permutation of a discrete hypercube [n]t. As applications we show that in the limit of large t (resp. n) almost all permutations are not stable, thus proving Conj. 12.5 of Brenti and Conti [Adv. Math. 381 (2021), p. 60], characterize (and enumerate) stable quadratic 4 and 5-cycles, as well as a notable class of stable quadratic r-cycles, i.e. those admitting a compatible cyclic factorization by stable transpositions. Some of our results use new combinatorial concepts that may be of independent interest.
2024
automorphism; Cuntz algebra; cycle; enumeration; Permutation; rank; stable permutation
01 Pubblicazione su rivista::01a Articolo in rivista
CUNTZ ALGEBRA AUTOMORPHISMS: GRAPHS AND STABILITY OF PERMUTATIONS / Brenti, F.; Conti, R.; Nenashev, G.. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - 377:12(2024), pp. 8433-8476. [10.1090/tran/9159]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1730959
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