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Individual Gap Measures from Generalized Zeckendorf Degompositions Cover

Individual Gap Measures from Generalized Zeckendorf Degompositions

Open Access
|Jul 2017

References

  1. ALPERT. H.: Differences of multiple Fibonacci numbers. Integers: Electronic: Journal of Combinatorial Number Theory 9 (2009). 745-749.10.1515/INTEG.2009.061
  2. BECKWITH. O.-BOWER. A.-GAUDET. L.-INSOFT. R.-LI. S - MILLER. S. J.-TOSTESON, P.: The average gap distribution for generalized Zeckendorf decompositions. Fibonacc i Quart. 51 (2013). 13 27.
  3. BOWER. A.-INSOFT. R. -LI. S.-MILLER. S. .1.-TOSTESON. P.: Distribution of gaps between summands in Generalized Zeckendorf decompositions (with an appendix on Extensions to Initial Segments with Iddo Ben-Ari). .1. Comb in. Theory Ser. A. 135 (2015). 130 160.10.1016/j.jcta.2015.04.005
  4. CATRAL, M.-FORD. P. HARRIS. P. E-MILLER, S. .1.- NELSON. D. - PAN. Z.-XU. H.: New behavior in legal decompositions arising from non- positive linear recurrences. 2016. https://arxiv.org/abs/1606.09309
  5. DAYKIN, D. E.: Representation of natural numbers as sums of generalized Fibonacci numbers. .1. Loud. Math. Soc. 35 (I960). 143 160.10.1112/jlms/s1-35.2.143
  6. DEMONTIGNY. P. DO.T. KULKARNI. A. MILLER . S..I. MOON.D. VARMA. U.: Generalizing Zeckendorf’s theorem to f-decompositions. .1. Number Theory 141 (2014), 136-158.10.1016/j.jnt.2014.01.028
  7. DEMONTIGNY. P. DO.T. KULKARNI. A.-MILLER. S. J.-VARMA. U.: A generalization of Fibonacci far-difference representations and Gaussian be¬havior. Fibonacci Quarterly 52 (2014). no. 3. 247 273.
  8. DORWARD. R.-FORD. P.-FOURAKIS, E - HARRIS. P. E. MILLER . S. .1.- PALSSON. E.-PAUGH. H.: A Generalization of Zeckendorf’s theorem via circumscribed m-gons, preprint.
  9. DRMOTA, M.-GAJDOSIK, .1.: The distribution of the sum-of-digits function .1. Tlieor. Nombres Bordeaux 10 (1998). no. 1. 17 32.
  10. FRISTEDT. B. E.-GRAY. L. F.: A Modern Approach to Probability Theory. Birkhauser. Boston 1996.10.1007/978-1-4899-2837-5
  11. GRABNER, P. .7.- TICHY. R. F. : Contributions to digit expansions with re¬spect to linear recurrences. .7. Number Theory 36 (1990). no. 2. 160-169.
  12. GRABNER. P. J.-TICHY. R. F.-NEMES. I.- PETHÔ. A.: Generalized Zeckendorf expansions, Appl. Math. Lett. 7 (1994). no. 2. 25-28. 10.1016/0893-9659(94)90025-6
  13. LAMBERGER. M. THUSWALDNER. .7. M.: Distribution properties of digital expansions arising from linear recurrences, Math. Slovaca 53 (2003). no. 1. 1 20.
  14. MILLER, S. .7.-WANG. Y.: From Fibonacci numbers to central limit type the¬orems, Journal of Combin. Theory Ser. A 119 (2012). no. 7. 1398 1413.
  15. STEINER. W.: Parry expansions of polynomial sequences, Integers 2 (20|J2). Paper Al l.
  16. STEINER. W.: The joint distribution of greedy and lazy Fibonacci expansions, Fibonacci Quart. 43 (2005). 60-69.
  17. ZECKENDORF. E.: Représentation des nombres naturels par une somme des nombres de Fibonacci ou de nombres de Lucas, Bull. Soc. Roy. Sci. de; Liège 41 ( 1972). 179 182.
DOI: https://doi.org/10.1515/udt-2017-0002 | Journal eISSN: 2309-5377 | Journal ISSN: 1336-913X
Language: English
Page range: 27 - 36
Submitted on: Aug 1, 2015
Accepted on: Dec 14, 2015
Published on: Jul 22, 2017
Published by: Slovak Academy of Sciences, Mathematical Institute
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 2017 Robert Dorward, Pari L. Ford, Eva Fourakis, Pamela E. Harris, Steven. J. Miller, Eyvindur A. Palsson, Hannah Paugh, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.