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On the dual complexity and spectra of some combinatorial functions
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXVIII, Tome 462 (2017), pp. 112-121

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In a recent paper, A. M. Vershik and the author started the study of representation-theoretic aspects of well-known combinatorial functions on the symmetric groups $\mathfrak S_n$. The note presents a series of further results in this direction. 
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     author = {N. V. Tsilevich},
     title = {On the dual complexity and spectra of some combinatorial functions},
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N. V. Tsilevich. On the dual complexity and spectra of some combinatorial functions. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXVIII, Tome 462 (2017), pp. 112-121. http://geodesic.mathdoc.fr/item/ZNSL_2017_462_a6/