نتایج جستجو برای: Fibonacci identities

تعداد نتایج: 27697  

Journal: :bulletin of the iranian mathematical society 2015
l. connell m. levine b. mathes j. sukiennik

we introduce a matricial toeplitz transform and prove that the toeplitz transform of a second order recurrence sequence is another second order recurrence sequence. we investigate the injectivity of this transform and show how this distinguishes the fibonacci sequence among other recurrence sequences. we then obtain new fibonacci identities as an application of our transform.

We introduce a matricial Toeplitz transform and prove that the Toeplitz transform of a second order recurrence sequence is another second order recurrence sequence. We investigate the injectivity of this transform and show how this distinguishes the Fibonacci sequence among other recurrence sequences. We then obtain new Fibonacci identities as an application of our transform.

2004
Mario Catalani

This note is dedicated to Professor Gould. The aim is to show how the identities in his book ”Combinatorial Identities” can be used to obtain identities for Fibonacci and Lucas polynomials. In turn these identities allow to derive a wealth of numerical identities for Fibonacci and Lucas numbers.

2017
Yogesh Kumar Gupta Mamta Singh

In [3], H. Belbachir and F. Bencherif generalize to bivariate polynomials of Fibonacci and Lucas, properties obtained for Chebyshev polynomials. They prove that the coordinates of the bivariate polynomials over appropriate basis are families of integers satisfying remarkable recurrence relations. [7], Mario Catalani define generalized bivariate polynomials, from which specifying initial conditi...

2017
Reza Kahkeshani

We know that the Fibonacci numbers count the tilings of a (1×n)-board by squares and dominoes, or equivalently, the number of tilings of a (2×n)-board by dominoes. We use the tilings of a (2×n)-board by colored unit squares and dominoes to obtain some new combinatorial identities. They are generalization of some known combinatorial identities and in the special case give us the Fibonacci identi...

2009
TROELS WINDFELDT

We generalize both the Fibonacci and Lucas numbers to the context of graph colorings, and prove some identities involving these numbers. As a corollary we obtain new proofs of some known identities involving Fibonacci numbers such as Fr+s+t = Fr+1Fs+1Ft+1 + FrFsFt − Fr−1Fs−1Ft−1.

2009
Troels Windfeldt

We generalize both the Fibonacci and Lucas numbers to the context of graphcolorings, and prove some identities involving these numbers. As a corollary we obtain newproofs of some known identities involving Fibonacci numbers such asFr+s+t = Fr+1Fs+1Ft+1 + FrFsFt − Fr−1Fs−1Ft−1.

2008
CHRISTOPHER J. HILLAR TROELS WINDFELDT

We generalize both the Fibonacci and Lucas numbers to the context of graph colorings, and prove some identities involving these numbers. As a corollary we obtain new proofs of some known identities involving Fibonacci numbers such as Fr+s+t = Fr+1Fs+1Ft+1 + FrFsFt − Fr−1Fs−1Ft−1.

Journal: :Eur. J. Comb. 2009
Adam M. Goyt Bruce E. Sagan

We consider the set partition statistics ls and rb introduced by Wachs and White and investigate their distribution over set partitions avoiding certain patterns. In particular, we consider those set partitions avoiding the pattern 13/2, Πn(13/2), and those avoiding both 13/2 and 123, Πn(13/2, 123). We show that the distribution over Πn(13/2) enumerates certain integer partitions, and the distr...

2008
TROELS WINDFELDT

We generalize both the Fibonacci and Lucas numbers to the context of graph colorings, and prove some identities involving these numbers. As a corollary we obtain new proofs of some known identities involving Fibonacci numbers such as Fr+s+t = Fr+1Fs+1Ft+1 + FrFsFt − Fr−1Fs−1Ft−1.

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