Results 1 
6 of
6
A new class of qFibonacci polynomials
 Electron. J. Combin. 10 (2003), Research Paper
, 2003
"... We introduce a new qanalogue of the Fibonacci polynomials and derive some of its properties. Extra attention is paid to a special case which has some interesting connections with Euler's pentagonal number theorem. 1 ..."
Abstract

Cited by 11 (1 self)
 Add to MetaCart
We introduce a new qanalogue of the Fibonacci polynomials and derive some of its properties. Extra attention is paid to a special case which has some interesting connections with Euler's pentagonal number theorem. 1
Parity theorems for statistics on domino arrangements
 ELECTRON J. COMBIN
, 2005
"... We study special values of Carlitz’s qFibonacci and qLucas polynomials Fn(q,t) and Ln(q,t). Brief algebraic and detailed combinatorial treatments are presented, the latter based on the fact that these polynomials are bivariate generating functions for a pair of statistics defined, respectively, on ..."
Abstract

Cited by 8 (4 self)
 Add to MetaCart
We study special values of Carlitz’s qFibonacci and qLucas polynomials Fn(q,t) and Ln(q,t). Brief algebraic and detailed combinatorial treatments are presented, the latter based on the fact that these polynomials are bivariate generating functions for a pair of statistics defined, respectively, on linear and circular domino arrangements.
qanalogs of some congruences involving Catalan numbers, prepint
"... We provide some variations on the GreeneKrammer’s identity which involve qCatalan numbers. Our method reveals a curious analogy between these new identities and some congruences modulo a prime. 1 ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
We provide some variations on the GreeneKrammer’s identity which involve qCatalan numbers. Our method reveals a curious analogy between these new identities and some congruences modulo a prime. 1
Multiple extensions of a finite Euler’s pentagonal number theorem and the Lucas formulas
, 707
"... Abstract. Motivated by the resemblance of a multivariate series identity and a finite analogue of Euler’s pentagonal number theorem, we study multiple extensions of the latter formula. In a different direction we derive a common extension of this multivariate series identity and two formulas of Luca ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
Abstract. Motivated by the resemblance of a multivariate series identity and a finite analogue of Euler’s pentagonal number theorem, we study multiple extensions of the latter formula. In a different direction we derive a common extension of this multivariate series identity and two formulas of Lucas. Finally we give a combinatorial proof of Lucas ’ formulas. Keywords: qbinomial coefficient, qChuVandermonde formula, Euler’s pentagonal number theorem, Lucas ’ formulas MR Subject Classifications: 05A10; 11B65
Periodicity and parity theorems for a statistic on rmino arrangements
 J. Integer Seq
, 2006
"... We study polynomial generalizations of the rFibonacci and rLucas sequences which arise in connection with a certain statistic on linear and circular rmino arrangements, respectively. By considering special values of these polynomials, we derive periodicity and parity theorems for this statistic o ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
We study polynomial generalizations of the rFibonacci and rLucas sequences which arise in connection with a certain statistic on linear and circular rmino arrangements, respectively. By considering special values of these polynomials, we derive periodicity and parity theorems for this statistic on the respective structures. 1
What’s experimental about experimental mathematics? ∗
, 2008
"... From a philosophical viewpoint, mathematics has often and traditionally been distinguished from the natural sciences by its formal nature and emphasis on deductive reasoning. Experiments — one of the corner stones of most modern natural science — have had no role to play in mathematics. However, dur ..."
Abstract
 Add to MetaCart
From a philosophical viewpoint, mathematics has often and traditionally been distinguished from the natural sciences by its formal nature and emphasis on deductive reasoning. Experiments — one of the corner stones of most modern natural science — have had no role to play in mathematics. However, during the last three decades, high speed computers and sophisticated software packages such as Maple and Mathematica have entered into the domain of pure mathematics, bringing with them a new experimental flavor. They have opened up a new approach in which computerbased tools are used to experiment with the mathematical objects in a dialogue with more traditional methods of formal rigorous proof. At present, a subdiscipline of experimental mathematics is forming with its own research problems, methodology, conferences, and journals. In this paper, I first outline the role of the computer in the mathematical experiment and briefly describe the impact of high speed computing on mathematical research within the emerging subdiscipline of experimental mathematics. I then consider in more detail the epistemological claims put forward within experimental mathematics and comment on some of the discussions that experimental mathematics has provoked within the mathematical community in recent years. In the second part of the paper, I suggest the notion of exploratory experimentation as a possible framework for understanding experimental mathematics. This is illustrated by discussing the socalled PSLQ algorithm.