Add to ORKGCombinatorial techniques can frequently provide satisfying “explanations” of various mathematical phenomena. In this thesis, we seek to explain a number of well known number theoretic congruences using combinatorial methods. Many of the results we prove involve the Fibonacci sequence and its generalizations
The Fibonacci Numbers are one of the most intriguing sequences in mathematics. I present generalizat...
Mathematics is the science of patterns, and mathematicians attempt to understand these patterns and ...
[[sponsorship]]數學研究所[[note]]已出版;[SCI];有審查制度;具代表性[[note]]http://gateway.isiknowledge.com/gateway/Gate...
We provide elementary combinatorial proofs of several Fibonacci and Lucas number identities left ope...
We provide a list of simple looking identities that are still in need of combinatorial proof
The Fibonomial numbers are defined by \[ \begin{bmatrix}n \\ k \end{bmatrix} = \frac{\prod_{i=n-k+...
Fibonacci numbers arise in the solution of many combinatorial problems. They count the number of bin...
We give a combinatorial proof of an elementary property of generalized Lucas polynomials, inspired b...
Introduction and Statement of Problem The idea of congruence, introduced by Carl Guass, has many app...
The Fibonacci Numbers are one of the most intriguing sequences in mathematics. I present generalizat...
The Fibonomial numbers are defined by \[ \begin{bmatrix}n \\ k \end{bmatrix} = \frac{\prod_{i=n-k+...
In this diploma thesis, the combinatorial proofs of Fibonacci and related identities are discussed. ...
In this paper we explore generalized “$r$-Fibonacci Numbers” using a combinatorial “tiling” interpre...
A bijective proof is given for the following theorem: the number of compositions of n into odd parts...
We show that a congruence discovered by George E. Andrews in 1969 for the Fibonacci quotient directl...
The Fibonacci Numbers are one of the most intriguing sequences in mathematics. I present generalizat...
Mathematics is the science of patterns, and mathematicians attempt to understand these patterns and ...
[[sponsorship]]數學研究所[[note]]已出版;[SCI];有審查制度;具代表性[[note]]http://gateway.isiknowledge.com/gateway/Gate...
We provide elementary combinatorial proofs of several Fibonacci and Lucas number identities left ope...
We provide a list of simple looking identities that are still in need of combinatorial proof
The Fibonomial numbers are defined by \[ \begin{bmatrix}n \\ k \end{bmatrix} = \frac{\prod_{i=n-k+...
Fibonacci numbers arise in the solution of many combinatorial problems. They count the number of bin...
We give a combinatorial proof of an elementary property of generalized Lucas polynomials, inspired b...
Introduction and Statement of Problem The idea of congruence, introduced by Carl Guass, has many app...
The Fibonacci Numbers are one of the most intriguing sequences in mathematics. I present generalizat...
The Fibonomial numbers are defined by \[ \begin{bmatrix}n \\ k \end{bmatrix} = \frac{\prod_{i=n-k+...
In this diploma thesis, the combinatorial proofs of Fibonacci and related identities are discussed. ...
In this paper we explore generalized “$r$-Fibonacci Numbers” using a combinatorial “tiling” interpre...
A bijective proof is given for the following theorem: the number of compositions of n into odd parts...
We show that a congruence discovered by George E. Andrews in 1969 for the Fibonacci quotient directl...
The Fibonacci Numbers are one of the most intriguing sequences in mathematics. I present generalizat...
Mathematics is the science of patterns, and mathematicians attempt to understand these patterns and ...
[[sponsorship]]數學研究所[[note]]已出版;[SCI];有審查制度;具代表性[[note]]http://gateway.isiknowledge.com/gateway/Gate...