@unpublished(Ambroz-Dombek-Masakova-Pelantova,
 author       = "P.~Ambro{\v {z}} and D.~Dombek and Z.~Mas{\'a}kov{\'a} and E.~Pelantov{\'a}",
 title        = "Numbers with integer expansion in the numeration system with negative base",
 note         = "ArXiv:0912.4597v3 [math.NT]",
)
@article(Burdik-Frougny-Gazeau-Krejcar98,
 author       = "{\v {C}}.~Burd{\'{\i }}k and C.~Frougny and J.~P. Gazeau and R.~Krejcar",
 year         = "1998",
 title        = "Beta-integers as natural counting systems for quasicrystals",
 journal      = "J. Phys. A",
 volume       = "31",
 number       = "30",
 pages        = "6449--6472",
 doi          = "10.1088/0305-4470/31/30/011",
)
@unpublished(Dombek-Masakova-Pelantova,
 author       = "D.~Dombek and Z.~Mas{\'a}kov{\'a} and E.~Pelantov{\'a}",
 title        = "Number representation using generalized $(-\beta )$-transformation",
 note         = "ArXiv:1102.3079v1 [cs.DM]",
)
@article(Gora07,
 author       = "P.~G{\'o}ra",
 year         = "2007",
 title        = "Invariant densities for generalized {$\beta $}-maps",
 journal      = "Ergodic Theory Dynam. Systems",
 volume       = "27",
 number       = "5",
 pages        = "1583--1598",
 doi          = "10.1017/S0143385707000053",
)
@article(Ito-Sadahiro09,
 author       = "S.~Ito and T.~Sadahiro",
 year         = "2009",
 title        = "Beta-expansions with negative bases",
 journal      = "Integers",
 volume       = "9",
 pages        = "A22, 239--259",
 doi          = "10.1515/INTEG.2009.023",
)
@unpublished(Liao-Steiner,
 author       = "L.~Liao and W.~Steiner",
 title        = "Dynamical properties of the negative beta-transformation",
 note         = "ArXiv:1101.2366v2 [math.DS]",
)
@article(Parry60,
 author       = "W.~Parry",
 year         = "1960",
 title        = "On the {$\beta $}-expansions of real numbers",
 journal      = "Acta Math. Acad. Sci. Hungar.",
 volume       = "11",
 pages        = "401--416",
 doi          = "10.1007/BF02020954",
)
@unpublished(Steiner,
 author       = "W.~Steiner",
 title        = "On the structure of ($-\beta $)-integers",
 note         = "ArXiv:1011.1755v2 [math.NT]",
)