Download Applications of Fibonacci Numbers: Volume 4 Proceedings of by Peter G. Anderson (auth.), G. E. Bergum, A. N. Philippou, A. PDF

By Peter G. Anderson (auth.), G. E. Bergum, A. N. Philippou, A. F. Horadam (eds.)

This ebook comprises thirty-three papers from one of the thirty-eight papers provided on the Fourth overseas convention on Fibonacci Numbers and Their functions which used to be held at Wake wooded area collage, Winston-Salem, North Carolina from July 30 to August three, 1990. those papers were chosen after a cautious evaluation via renowned referees within the box, they usually variety from straight forward quantity idea to likelihood and data. The Fibonacci numbers and recurrence family members are their unifying bond. it really is expected that this booklet, like its 3 predecessors, could be valuable to analyze employees and graduate scholars attracted to the Fibonacci numbers and their purposes. March 1, 1991 The Editors Gerald E. Bergum South Dakota kingdom college Brookings, South Dakota, U. S. A. Alwyn F. Horadam college of recent England Armidale, N. S. W. , Australia Andreas N. Philippou Minister of schooling Ministry of schooling Nicosia, Cyprus xv THE ORGANIZING COMMITTEES neighborhood COMMITTEE foreign COMMITTEE Howard, Fred T. , Co-Chair Horadam, A. F. (Australia), Co-Chair Waddill, Marcellus E. , Co-Chair Philippou, A. N. (Cyprus), Co-Chair Hayashi, Elmer okay. Ando, S. (Japan) Bergum, G. E. (U. S. A. ) Vaughan, Theresa Harrell, Deborah Bicknell-Johnson, M. B. (U. S. A. ) Campbell, Colin (Scotland) Filipponi, Piero (Italy) Kiss, P. (Hungary) Turner, J. C. (New Zealand) xvii record OF individuals TO THE convention *ALFORD, CECIL zero. , (coauthor Daniel C. Fielder) "Pascal's Triangle: most sensible Gun or simply one of many Gang?" *ANDERSON, PETER G. , "A Fibonacci-Based Pseudo-Random quantity Generator.

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Additional resources for Applications of Fibonacci Numbers: Volume 4 Proceedings of ‘The Fourth International Conference on Fibonacci Numbers and Their Applications’, Wake Forest University, N.C., U.S.A., July 30–August 3, 1990

Example text

3) E. G. Straus, in 1976, in a private letter to Arkin, described how he constructed a 7x7x7 perfect magic cube. This may be the lowest possible order of a perfect Latin 3-cube [5]. (4) In 1985, Arkin superimposed 6 orthogonal Latin cubes of order 7 to form 20 separate Latin 3-cubes [1]. (5) A perfect 4-dimensional hypercube of order 7 was constructed at West Point in 1989 [2]. LATIN K-CUBE OF ORDER N A Latin square of order n is an nxn square in which each of the numbers 0, 1, ... , n - 1 occurs exactly once in each row and exactly once in each column.

Be a SDS, and let be any entry inside the generalized modified Pascal triangle defined in Ando [I]. If A, B, C, D, E, and F are six entries surrounding it as in example 1, then we have an LCM equality km {A, C, E} = km {B, D, F} (18) instead of GCD equality (7). A p-adic proof of (18) was shown in [I]. We will give here a nonp-adic proof. If we use (16), we can equivalently express this relation as in terms of the GCD of rational numbers. For the case an=n (n=l, 2, 3, .. '), Sato [81 gave a simple proof by showing the linear relations 14 S.

N -1)(n -1) occurs. Thus 120 00 11 22 201 superimpose to 12 20 01 120 02 10 012 012 and 201 21 and therefore are orthogonal squares of order 3. A set of Latin squares of order n is orthogonal if every two of them are orthogonal. As an example the 4x4 square of triples 000 111 222 333 123 032 301 210 231 320 013 102 312 203 130 021 represents three mutually orthogonal squares of order 4 since each of the 16 pairs 00, 01, ... , 33 occurs in each of the three possible positions among the 16 triples.

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