On three questions concerning -polynomials
Michael Filaseta[1]; Carrie Finch[1]; Charles Nicol[1]
- [1] Mathematics Department University of South Carolina Columbia, SC 29208, USA
Journal de Théorie des Nombres de Bordeaux (2006)
- Volume: 18, Issue: 2, page 357-370
- ISSN: 1246-7405
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topFilaseta, Michael, Finch, Carrie, and Nicol, Charles. "On three questions concerning ${0,1}$-polynomials." Journal de Théorie des Nombres de Bordeaux 18.2 (2006): 357-370. <http://eudml.org/doc/249611>.
@article{Filaseta2006,
abstract = {We answer three reducibility (or irreducibility) questions for $0,1$-polynomials, those polynomials which have every coefficient either $0$ or $1$. The first concerns whether a naturally occurring sequence of reducible polynomials is finite. The second is whether every nonempty finite subset of an infinite set of positive integers can be the set of positive exponents of a reducible $0,1$-polynomial. The third is the analogous question for exponents of irreducible $0,1$-polynomials.},
affiliation = {Mathematics Department University of South Carolina Columbia, SC 29208, USA; Mathematics Department University of South Carolina Columbia, SC 29208, USA; Mathematics Department University of South Carolina Columbia, SC 29208, USA},
author = {Filaseta, Michael, Finch, Carrie, Nicol, Charles},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {0,1-polynomials},
language = {eng},
number = {2},
pages = {357-370},
publisher = {Université Bordeaux 1},
title = {On three questions concerning $\{0,1\}$-polynomials},
url = {http://eudml.org/doc/249611},
volume = {18},
year = {2006},
}
TY - JOUR
AU - Filaseta, Michael
AU - Finch, Carrie
AU - Nicol, Charles
TI - On three questions concerning ${0,1}$-polynomials
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2006
PB - Université Bordeaux 1
VL - 18
IS - 2
SP - 357
EP - 370
AB - We answer three reducibility (or irreducibility) questions for $0,1$-polynomials, those polynomials which have every coefficient either $0$ or $1$. The first concerns whether a naturally occurring sequence of reducible polynomials is finite. The second is whether every nonempty finite subset of an infinite set of positive integers can be the set of positive exponents of a reducible $0,1$-polynomial. The third is the analogous question for exponents of irreducible $0,1$-polynomials.
LA - eng
KW - 0,1-polynomials
UR - http://eudml.org/doc/249611
ER -
References
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- H. Tverberg, On the irreducibility of the trinomials . Math. Scand. 8 (1960), 121–126. Zbl0097.00801MR124314
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