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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.