# Multigeometric sequences and Cantorvals

Artur Bartoszewicz; Małgorzata Filipczak; Emilia Szymonik

Open Mathematics (2014)

- Volume: 12, Issue: 7, page 1000-1007
- ISSN: 2391-5455

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topArtur Bartoszewicz, Małgorzata Filipczak, and Emilia Szymonik. "Multigeometric sequences and Cantorvals." Open Mathematics 12.7 (2014): 1000-1007. <http://eudml.org/doc/269306>.

@article{ArturBartoszewicz2014,

abstract = {For a sequence x ∈ l 10, one can consider the achievement set E(x) of all subsums of series Σn=1∞ x(n). It is known that E(x) has one of the following structures: a finite union of closed intervals, a set homeomorphic to the Cantor set, a set homeomorphic to the set T of subsums of Σn=1∞ x(n) where c(2n − 1) = 3/4n and c(2n) = 2/4n (Cantorval). Based on ideas of Jones and Velleman [Jones R., Achievement sets of sequences, Amer. Math. Monthly, 2011, 118(6), 508–521] and Guthrie and Nymann [Guthrie J.A., Nymann J.E., The topological structure of the set of subsums of an infinite series, Colloq. Math., 1988, 55(2), 323–327] we describe families of sequences which contain, according to our knowledge, all known examples of x with E(x) being Cantorvals.},

author = {Artur Bartoszewicz, Małgorzata Filipczak, Emilia Szymonik},

journal = {Open Mathematics},

keywords = {Multigeometric sequence; Achievement set of sequence; M-Cantorval; multigeometric sequence; achievement set of sequence; cantorval},

language = {eng},

number = {7},

pages = {1000-1007},

title = {Multigeometric sequences and Cantorvals},

url = {http://eudml.org/doc/269306},

volume = {12},

year = {2014},

}

TY - JOUR

AU - Artur Bartoszewicz

AU - Małgorzata Filipczak

AU - Emilia Szymonik

TI - Multigeometric sequences and Cantorvals

JO - Open Mathematics

PY - 2014

VL - 12

IS - 7

SP - 1000

EP - 1007

AB - For a sequence x ∈ l 10, one can consider the achievement set E(x) of all subsums of series Σn=1∞ x(n). It is known that E(x) has one of the following structures: a finite union of closed intervals, a set homeomorphic to the Cantor set, a set homeomorphic to the set T of subsums of Σn=1∞ x(n) where c(2n − 1) = 3/4n and c(2n) = 2/4n (Cantorval). Based on ideas of Jones and Velleman [Jones R., Achievement sets of sequences, Amer. Math. Monthly, 2011, 118(6), 508–521] and Guthrie and Nymann [Guthrie J.A., Nymann J.E., The topological structure of the set of subsums of an infinite series, Colloq. Math., 1988, 55(2), 323–327] we describe families of sequences which contain, according to our knowledge, all known examples of x with E(x) being Cantorvals.

LA - eng

KW - Multigeometric sequence; Achievement set of sequence; M-Cantorval; multigeometric sequence; achievement set of sequence; cantorval

UR - http://eudml.org/doc/269306

ER -

## References

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