S. Akiyama, T. Borbely, H. Brunotte, A. Peth}o and J. M. Thuswaldner, Gen-
eralized radix representations and dynamical systems I, Acta Math. Hungar.,
108(3) (2005), 207-238.
S. Akiyama, H. Brunotte and A. Peth}o, Cubic CNS polynomials, notes on a
conjecture of W. J. Gilbert, J. Math. Anal. Appl., 281(1) (2003), 402-415.
S. Akiyama and A. Peth}o, On canonical number systems, Theoret. Comput.
Sci., 270(1-2) (2002), 921-933.
S. Akiyama and H. Rao, New criteria for canonical number systems, Acta
Arith., 111(1) (2004), 5-25.
S. Akiyama and K. Scheicher, Symmetric shift radix systems and nite expan-
sions, Math. Pannon., 18(1) (2007), 101-124.
G. Barat, V. Berthe, P. Liardet and J. Thuswaldner, Dynamical directions in
numeration, Numeration, pavages, substitutions, Ann. Inst. Fourier (Grenoble),
56(7) (2006), 1987-2092.
V. Berthe, Numeration and discrete dynamical systems, Computing, 94(2-4)
(2012), 369-387.
T. Borbely, Altalanostott szamrendszerek, Master Thesis, University of Debrecen,
2003.
J. Borcea and P. Branden, The Lee-Yang and Polya-Schur programs II, The-
ory of stable polynomials and applications, Comm. Pure Appl. Math., 62(12)
(2009), 1595-1631.
H. Brunotte, Characterization of CNS trinomials, Acta Sci. Math. (Szeged),
68(3-4) (2002), 673-679.
H. Brunotte, On the roots of expanding integer polynomials, Acta Math. Acad.
Paedagog. Nyhazi. (N.S.), 27(2) (2011), 161-171.
H. Brunotte, A unied proof of two classical theorems on CNS polynomials,
Integers, 12(4) (2012), 709-721.
H. Brunotte, Unusual CNS polynomials, Math. Pannon., 24(1) (2013), 125-137.
[15] H. Brunotte, Small degree CNS polynomials with dominant condition, Math.
Pannon., 25(1) (2014/15), 113-133.
P. Burcsi and A. Kovacs, Exhaustive search methods for CNS polynomials,
Monatsh. Math., 155(3-4) (2008), 421-430.
A. Chen, On the reducible quintic complete base polynomials, J. Number Theory,
129(1) (2009), 220-230.
A. Dubickas, Roots of polynomials with dominant term, Int. J. Number Theory,
7(5) (2011), 1217-1228.
L. German and A. Kovacs, On number system constructions, Acta Math. Hungar.,
115(1-2) (2007), 155-167.
W. J. Gilbert, Radix representations of quadratic elds, J. Math. Anal. Appl.,
83(1) (1981), 264-274.
V. Grunwald, Intorno all'aritmetica dei sistemi numerici a base negativa con
particolare riguardo al sistema numerico a base negativo-decimale per lo studio
delle sue analogie coll'aritmetica ordinaria (decimale), Giornale di matematiche
di Battaglini, 23 (1885), 203-221.
D. M. Kane, Generalized base representations, J. Number Theory, 120(1)
(2006), 92-100.
I. Katai and B. Kovacs, Kanonische Zahlensysteme in der Theorie der
quadratischen algebraischen Zahlen, Acta Sci. Math. (Szeged), 42 (1980), 99-
107.
I. Katai and B. Kovacs, Canonical number systems in imaginary quadratic
elds, Acta Math. Acad. Sci. Hungar., 37(1-3) (1981), 159-164.
I. Katai and J. Szabo, Canonical number systems for complex integers, Acta
Sci. Math. (Szeged), 37(3-4) (1975), 255-260.
D. E. Knuth, An imaginary number system, Comm. ACM, 3 (1960), 245-247.
B. Kovacs, Canonical number systems in algebraic number elds, Acta Math.
Acad. Sci. Hungar., 37(4) (1981), 405-407.
A. Kovacs, Generalized binary number systems, Ann. Univ. Sci. Budapest.
Sect. Comput., 20 (2001), 195-206.
B. Kovacs and A. Peth}o, Number systems in integral domains, especially in
orders of algebraic number elds, Acta Sci. Math. (Szeged), 55(3-4) (1991),
287-299.
A. Peth}o, On a polynomial transformation and its application to the construc-
tion of a public key cryptosystem, in Computational number theory (Debrecen,
1989), de Gruyter, Berlin, (1991), 31-43.
A. Peth}o, Private communication, 2000.
A. Peth}o, Connections between power integral bases and radix representations
in algebraic number elds, in Proceedings of the 2003 Nagoya Conference
\Yokoi-Chowla Conjecture and Related Problems", S. Katayama, C. Levesque,
and T. Nakahara, eds., Saga Univ., Saga, (2004), 115-125.
K. Scheicher and J. M. Thuswaldner, On the characterization of canonical
number systems, Osaka J. Math., 41(2) (2004), 327-351.
P. Surer, "-shift radix systems and radix representations with shifted digit sets,
Publ. Math. Debrecen, 74(1-2) (2009), 19-43.
A. Tatrai, Parallel implementations of Brunotte's algorithm, J. Parallel Distrib.
Comput., 71(4) (2011), 565-572.
Some comments on Akiyama's conjecture on CNS polynomials
Year 2018,
Volume: 23 Issue: 23, 167 - 175, 11.01.2018
S. Akiyama, T. Borbely, H. Brunotte, A. Peth}o and J. M. Thuswaldner, Gen-
eralized radix representations and dynamical systems I, Acta Math. Hungar.,
108(3) (2005), 207-238.
S. Akiyama, H. Brunotte and A. Peth}o, Cubic CNS polynomials, notes on a
conjecture of W. J. Gilbert, J. Math. Anal. Appl., 281(1) (2003), 402-415.
S. Akiyama and A. Peth}o, On canonical number systems, Theoret. Comput.
Sci., 270(1-2) (2002), 921-933.
S. Akiyama and H. Rao, New criteria for canonical number systems, Acta
Arith., 111(1) (2004), 5-25.
S. Akiyama and K. Scheicher, Symmetric shift radix systems and nite expan-
sions, Math. Pannon., 18(1) (2007), 101-124.
G. Barat, V. Berthe, P. Liardet and J. Thuswaldner, Dynamical directions in
numeration, Numeration, pavages, substitutions, Ann. Inst. Fourier (Grenoble),
56(7) (2006), 1987-2092.
V. Berthe, Numeration and discrete dynamical systems, Computing, 94(2-4)
(2012), 369-387.
T. Borbely, Altalanostott szamrendszerek, Master Thesis, University of Debrecen,
2003.
J. Borcea and P. Branden, The Lee-Yang and Polya-Schur programs II, The-
ory of stable polynomials and applications, Comm. Pure Appl. Math., 62(12)
(2009), 1595-1631.
H. Brunotte, Characterization of CNS trinomials, Acta Sci. Math. (Szeged),
68(3-4) (2002), 673-679.
H. Brunotte, On the roots of expanding integer polynomials, Acta Math. Acad.
Paedagog. Nyhazi. (N.S.), 27(2) (2011), 161-171.
H. Brunotte, A unied proof of two classical theorems on CNS polynomials,
Integers, 12(4) (2012), 709-721.
H. Brunotte, Unusual CNS polynomials, Math. Pannon., 24(1) (2013), 125-137.
[15] H. Brunotte, Small degree CNS polynomials with dominant condition, Math.
Pannon., 25(1) (2014/15), 113-133.
P. Burcsi and A. Kovacs, Exhaustive search methods for CNS polynomials,
Monatsh. Math., 155(3-4) (2008), 421-430.
A. Chen, On the reducible quintic complete base polynomials, J. Number Theory,
129(1) (2009), 220-230.
A. Dubickas, Roots of polynomials with dominant term, Int. J. Number Theory,
7(5) (2011), 1217-1228.
L. German and A. Kovacs, On number system constructions, Acta Math. Hungar.,
115(1-2) (2007), 155-167.
W. J. Gilbert, Radix representations of quadratic elds, J. Math. Anal. Appl.,
83(1) (1981), 264-274.
V. Grunwald, Intorno all'aritmetica dei sistemi numerici a base negativa con
particolare riguardo al sistema numerico a base negativo-decimale per lo studio
delle sue analogie coll'aritmetica ordinaria (decimale), Giornale di matematiche
di Battaglini, 23 (1885), 203-221.
D. M. Kane, Generalized base representations, J. Number Theory, 120(1)
(2006), 92-100.
I. Katai and B. Kovacs, Kanonische Zahlensysteme in der Theorie der
quadratischen algebraischen Zahlen, Acta Sci. Math. (Szeged), 42 (1980), 99-
107.
I. Katai and B. Kovacs, Canonical number systems in imaginary quadratic
elds, Acta Math. Acad. Sci. Hungar., 37(1-3) (1981), 159-164.
I. Katai and J. Szabo, Canonical number systems for complex integers, Acta
Sci. Math. (Szeged), 37(3-4) (1975), 255-260.
D. E. Knuth, An imaginary number system, Comm. ACM, 3 (1960), 245-247.
B. Kovacs, Canonical number systems in algebraic number elds, Acta Math.
Acad. Sci. Hungar., 37(4) (1981), 405-407.
A. Kovacs, Generalized binary number systems, Ann. Univ. Sci. Budapest.
Sect. Comput., 20 (2001), 195-206.
B. Kovacs and A. Peth}o, Number systems in integral domains, especially in
orders of algebraic number elds, Acta Sci. Math. (Szeged), 55(3-4) (1991),
287-299.
A. Peth}o, On a polynomial transformation and its application to the construc-
tion of a public key cryptosystem, in Computational number theory (Debrecen,
1989), de Gruyter, Berlin, (1991), 31-43.
A. Peth}o, Private communication, 2000.
A. Peth}o, Connections between power integral bases and radix representations
in algebraic number elds, in Proceedings of the 2003 Nagoya Conference
\Yokoi-Chowla Conjecture and Related Problems", S. Katayama, C. Levesque,
and T. Nakahara, eds., Saga Univ., Saga, (2004), 115-125.
K. Scheicher and J. M. Thuswaldner, On the characterization of canonical
number systems, Osaka J. Math., 41(2) (2004), 327-351.
P. Surer, "-shift radix systems and radix representations with shifted digit sets,
Publ. Math. Debrecen, 74(1-2) (2009), 19-43.
A. Tatrai, Parallel implementations of Brunotte's algorithm, J. Parallel Distrib.
Comput., 71(4) (2011), 565-572.
Brunotte, H. (2018). Some comments on Akiyama’s conjecture on CNS polynomials. International Electronic Journal of Algebra, 23(23), 167-175. https://doi.org/10.24330/ieja.373660
AMA
Brunotte H. Some comments on Akiyama’s conjecture on CNS polynomials. IEJA. January 2018;23(23):167-175. doi:10.24330/ieja.373660
Chicago
Brunotte, Horst. “Some Comments on Akiyama’s Conjecture on CNS Polynomials”. International Electronic Journal of Algebra 23, no. 23 (January 2018): 167-75. https://doi.org/10.24330/ieja.373660.
EndNote
Brunotte H (January 1, 2018) Some comments on Akiyama’s conjecture on CNS polynomials. International Electronic Journal of Algebra 23 23 167–175.
IEEE
H. Brunotte, “Some comments on Akiyama’s conjecture on CNS polynomials”, IEJA, vol. 23, no. 23, pp. 167–175, 2018, doi: 10.24330/ieja.373660.
ISNAD
Brunotte, Horst. “Some Comments on Akiyama’s Conjecture on CNS Polynomials”. International Electronic Journal of Algebra 23/23 (January 2018), 167-175. https://doi.org/10.24330/ieja.373660.
JAMA
Brunotte H. Some comments on Akiyama’s conjecture on CNS polynomials. IEJA. 2018;23:167–175.
MLA
Brunotte, Horst. “Some Comments on Akiyama’s Conjecture on CNS Polynomials”. International Electronic Journal of Algebra, vol. 23, no. 23, 2018, pp. 167-75, doi:10.24330/ieja.373660.
Vancouver
Brunotte H. Some comments on Akiyama’s conjecture on CNS polynomials. IEJA. 2018;23(23):167-75.