Some comments on Akiyama's conjecture on CNS polynomials
It is well-known that in general polynomials lose their CNS property
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- S. Akiyama, Private communication, 2012.
- 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 uni ed 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.