[AGH]
Auslander, L., Green, L. and Hahn, F.. Flows on Homogeneous Spaces
*(Annals of Mathematics Studies, 53)*
. Princeton University Press, Princeton, NJ, 1963.

[B1]
Bergelson, V.. Ergodic Ramsey theory—An Update, Ergodic Theory of ℤ^{
d
}-Actions
*(London Mathematical Society Lecture Note Series, 228)*
. Cambridge University Press, Cambridge, 1996, pp. 1–61.

[B2]
Bergelson, V.. The multifarious Poincaré recurrence theorem. Descriptive Set Theory and Dynamical Systems
*(London Mathematical Society Lecture Note Series, 277)*
. Cambridge University Press, Cambridge, 2000, pp. 31–57.

[B3]
Bergelson, V.. Minimal idempotents and ergodic Ramsey theory. Topics in Dynamics and Ergodic Theory
*(London Mathematical Society Lecture Note Series, 310)*
. Cambridge University Press, Cambridge, 2003, pp. 8–39.

[B4]
Bergelson, V.. Ergodic Ramsey Theory
*(Contemporary Mathematics, 65)*
. American Mathematical Society, Providence, RI, 1987, pp. 63–87.

[BD]
Bergelson, V. and Downarowicz, T.. Large sets of integers and hierarchy of mixing properties of measure preserving systems. Colloq. Math.
110(1) (2008), 117–150.

[BFM]
Bergelson, V., Furstenberg, H. and McCutcheon, R.. IP-sets and polynomial recurrence. Ergod. Th. & Dynam. Sys.
16 (1996), 963–974.

[BFW]
Bergelson, V., Furstenberg, H. and Weiss, B.. Piecewise-Bohr sets of integers and combinatorial number theory. Topics in Discrete Mathematics
*(Algorithms and Combinatorics, 26)*
. Springer, Berlin, 2006, pp. 13–37.

[BHoK]
Bergelson, V., Host, B. and Kra, B.. Multiple recurrence and nilsequences., With an appendix by I. Ruzsa. Invent. Math.
160(2) (2005), 261–303.

[BL1]
Bergelson, V. and Leibman, A.. Set-polynomials and polynomial extension of the Hales–Jewett theorem. Ann. of Math. (2)
150 (1999), 33–75.

[BL2]
Bergelson, V. and Leibman, A.. Cubic averages and large intersections. Contemp. Math.
631 (2015), 5–20.

[BL3]
Bergelson, V. and Leibman, A.. IP
-recurrence and nilsystems. *Preprint*, 2016, arXiv:1604.02489.

[BLLe1]
Bergelson, V., Leibman, A. and Lesigne, E.. Weyl complexity of a system of polynomials, and constructions in combinatorial number theory. J. Anal. Math.
103 (2007), 47–92.

[BLLe2]
Bergelson, V., Leibman, A. and Lesigne, E.. Intersective polynomials and the polynomial Szemerédi theorem. Adv. Math.
219 (2008), 369–388.

[BM1]
Bergelson, V. and McCutcheon, R.. Central sets and a non-commutative Roth theorem. Amer. J. Math.
129(5) (2007), 1251–1275.

[BM2]
Bergelson, V. and McCutcheon, R.. Idempotent ultrafilters, multiple weak mixing and Szemerédi’s theorem for generalized polynomials. J. Anal. Math.
111 (2010), 77–130.

[F]
Frantzikinakis, N.. Multiple correlation sequences and nilsequences. Invent. Math.
202 (2015), 875–892.

[FK]
Frantzikinakis, N. and Kra, B.. Polynomial averages converge to the product of integrals. Israel J. Math.
148 (2005), 267–276.

[Fu]
Furstenberg, H.. Recurrence in Ergodic Theory and Combinatorial Number Theory. Princeton University Press, Princeton, NJ, 1981.

[FuW]
Furstenberg, H. and Weiss, B.. Topological dynamics and combinatorial number theory. J. D’Anal. Math.
34 (1978), 61–85.

[G]
Gillis, J.. Note on a property of measurable sets. J. Lond. Math. Soc. (2)
11(2) (1936), 139–141.

[H]
Hindman, N.. Finite sums from sequences within cells of a partition of ℕ. J. Combin. Theory Ser. A
17 (1974), 1–11.

[HoK1]
Host, B. and Kra, B.. Averaging along cubes. Modern Dynamical Systems and Applications. Cambridge University Press, Cambridge, 2004, pp. 123–144.

[HoK2]
Host, B. and Kra, B.. Non-conventional ergodic averages and nilmanifolds. Ann. of Math. (2)
161(1) (2005), 397–488.

[HoK3]
Host, B. and Kra, B.. Nil–Bohr sets of integers. Ergod. Th. & Dynam. Sys.
31 (2011), 113–142.

[HoKM]
Host, B., Kra, B. and Maass, A.. Complexity of nilsystems and systems lacking nilfactors. J. Anal. Math.
124 (2014), 261–295.

[Ke1]
Keynes, H. B.. Topological dynamics in coset transformation groups. Bull. Amer. Math. Soc. (N.S.)
72 (1966), 1033–1035.

[Ke2]
Keynes, H. B.. A study of the proximal relation in coset transformation groups. Trans. Amer. Math. Soc.
128 (1967), 389–402.

[Kh]
Khintchine, A. Y.. Eine Verschärfung des Poincaréschen ‘Wiederkehrsatzes’. Comput. Math.
1 (1934), 177–179.

[L1]
Leibman, A.. Pointwise convergence of ergodic averages, for polynomial sequences of translations on a nilmanifold. Ergod. Th. & Dynam. Sys.
25 (2005), 201–213.

[L2]
Leibman, A.. Pointwise convergence of ergodic averages, for polynomial actions of ℤ^{
d
} by translations on a nilmanifold. Ergod. Th. & Dynam. Sys.
25 (2005), 215–225.

[L3]
Leibman, A.. Convergence of multiple ergodic averages along polynomials of several variables. Israel J. Math.
146 (2005), 303–315.

[L4]
Leibman, A.. Rational sub-nilmanifolds of a compact nilmanifold. Ergod. Th. & Dynam. Sys.
26 (2006), 787–798.

[L5]
Leibman, A.. Orbits on a nilmanifold under the action of a polynomial sequence of translations. Ergod. Th. & Dynam. Sys.
27 (2007), 1239–1252.

[L6]
Leibman, A.. Orbit of the diagonal in the power of a nilmanifold. Trans. Amer. Math. Soc.
362 (2010), 1619–1658.

[L7]
Leibman, A.. Nilsequences, nul-sequences, and the multiple correlation sequences. Ergod. Th. & Dynam. Sys.
31 (2015), 176–191.

[M]
McCutcheon, R.. Private communications, 2015.

[MZ]
McCutcheon, R. and Zhou, J.. D sets and IP rich sets in ℤ. Fund. Math.
233 (2016), 71–82.

[Zi]
Ziegler, T.. Universal characteristic factors and Furstenberg averages. J. Amer. Math. Soc.
20 (2007), 53–97.