Integers with a maximal number of Fibonacci representations

نویسندگان

  • Petra Kocábová
  • Zuzana Masáková
  • Edita Pelantová
چکیده

We study the properties of the function R(n) which determines the number of representations of an integer n as a sum of distinct Fibonacci numbers Fk. We determine the maximum and mean values of R(n) for Fk ≤ n < Fk+1. Mathematics Subject Classification. 11A67, 11B39.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

EEH: AGGH-like public key cryptosystem over the eisenstein integers using polynomial representations

GGH class of public-key cryptosystems relies on computational problems based on the closest vector problem (CVP) in lattices for their security. The subject of lattice based cryptography is very active and there have recently been new ideas that revolutionized the field. We present EEH, a GGH-Like public key cryptosystem based on the Eisenstein integers Z [ζ3] where ζ3 is a primitive...

متن کامل

Non-Abelian Sequenceable Groups Involving ?-Covers

A non-abelian finite group is called sequenceable if for some positive integer , is -generated ( ) and there exist integers such that every element of is a term of the -step generalized Fibonacci sequence , , , . A remarkable application of this definition may be find on the study of random covers in the cryptography. The 2-step generalized sequences for the dihedral groups studi...

متن کامل

Robust transmission of unbounded strings using Fibonacci representations

Families of Fibonacci codes and Fibonacci representations are defined. Their main attributes are: (i) robustness, manifesting itself by the local containment of errors; (ii) simple encoding and and decoding. The main applica· tiOD explored is the transmission of binary strings whose length is in aD. unknown range, using robust Fibonacci representations instead of the conventional errorsensitive...

متن کامل

On the Usefulness of Fibonacci Compression Codes

Recent publications advocate the use of various variable length codes for which each codeword consists of an integral number of bytes in compression applications using large alphabets. This paper shows that another tradeoff with similar properties can be obtained by Fibonacci codes. These are fixed codeword sets, using binary representations of integers based on Fibonacci numbers of order m ≥ 2...

متن کامل

Generalizations of the Dual Zeckendorf Integer Representation Theorems—discovery by Fibonacci Trees and Word Patterns

In this paper we show how the two well-known integer representation theorems which are associated with the name of Zeckendorf may be generalized as dual systems by constructing colored tree sequences whose shade sets partition Z = {1, 2, . . . } . Many interesting properties of the representations can be observed directly from the tree diagrams, and the proofs of the properties can truly be sai...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • ITA

دوره 39  شماره 

صفحات  -

تاریخ انتشار 2005