TY - JOUR

T1 - SURVEY ON DEVIATIONS AND ARITHMETIC PROPERTIES OF COMBINATORIAL STATISTICS AFTER DYSON, ANDREWS, AND GARVAN

AU - Borozenets, N.E.

N1 - Export Date: 03 March 2026; Cited By: 1; Correspondence Address: N.E. Borozenets; Skoltech Igor Krichever Center for Advanced Studies, Moscow, Bld. 1, 30, Bolshoy Boulevard, 121205, Russian Federation; email: nikolayborozenets.spbumcs@gmail.com

PY - 2025

Y1 - 2025

N2 - In this survey, we overview the celebrated Ramanujan’s congruences modulo 5, 7 and 11 for the partition function and how the classical combinatorial statistics rank and crank introduced by Dyson, Andrews and Garvan explain them. We also present some recent results on the explicit calculation of the dissections of the deviations of rank and crank and how these computations help to deduce unexpected arithmetic properties of these combinatorial statistics. In addition, we posed some open problems in this area. Bibliography: 36 titles. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.

AB - In this survey, we overview the celebrated Ramanujan’s congruences modulo 5, 7 and 11 for the partition function and how the classical combinatorial statistics rank and crank introduced by Dyson, Andrews and Garvan explain them. We also present some recent results on the explicit calculation of the dissections of the deviations of rank and crank and how these computations help to deduce unexpected arithmetic properties of these combinatorial statistics. In addition, we posed some open problems in this area. Bibliography: 36 titles. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.

U2 - 10.1007/s10958-025-07900-3

DO - 10.1007/s10958-025-07900-3

M3 - Article

VL - 292

SP - 178

EP - 196

JO - Journal of Mathematical Sciences (Switzerland)

JF - Journal of Mathematical Sciences (Switzerland)

SN - 1072-3374

IS - 2

ER -