Global ETD Search

1	Functions of the Binomial Coefficient Plott, Sean 01 May 2008 (has links) The well known binomial coefficient is the building block of Pascal’s triangle. We explore the relationship between functions of the binomial coefficient and Pascal’s triangle, providing proofs of connections between Catalan numbers, determinants, non-intersecting paths, and Baxter permutations. Binomial Coefficient Functions
2	Analogues of the Binomial Coefficient Theorems of Gauss and Jacobi Al-Shaghay, Abdullah 20 March 2014 (has links) Two of the more well known congruences for binomial coefficients modulo p, due to Gauss and Jacobi, are related to the representation of an odd prime (or an integer multiple of the odd prime) p as a sum of two squares (or an integer linear combination of two squares). These two congruences, along with many others, have been extended to analogues modulo p^2 and are well documented. More recently, J. Cosgrave and K. Dilcher have extended the congruences of Gauss and Jacobi to analogues modulo p^3. In this thesis we discuss their methods as well as the potential of applying them to similar congruences found in the literature. Number Theory Binomial Coefficient
3	Applications of Generating Functions Tseng, Chieh-Mei 26 June 2007 (has links) Generating functions express a sequence as coefficients arising from a power series in variables. They have many applications in combinatorics and probability. In this paper, we will investigate the important properties of four kinds of generating functions in one variables: ordinary generating unction, exponential generating function, probability generating function and moment generating function. Many examples with applications in combinatorics and probability, will be discussed. Finally, some well-known contest problems related to generating functions will be addressed. moment generating function ordinary generating function exponential generating function probability generating function recurrence relation recurrence binomial coefficient binomial theorem weak law of large numbers central limit theorem moment probability distribution variance power series identities induction counting problem partition Fibonacci partial fractions sequence expectation convolution

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