三類條件分拆函數(shù)同余性質(zhì)的研究
[Abstract]:The congruence property of conditional partition function is one of the hot issues in combinatorial mathematics. It has extensive and close relations with many branches of mathematics, such as q-series, number theory, algebra, machine proving, and so on, and is widely and closely related in mathematics, physics, probability theory, etc. Computer science and other fields have important applications. In recent years, although mathematical researchers have discovered many congruence relations of conditional partition functions, there are still many problems to be solved. In this paper, the congruence properties of generalized Frobenius-6 coloring partition function, conditional Binary partition function and Overpartitions partition function are studied. The main work is as follows: in the first chapter, the background of conditional partition function is introduced. Research progress and research content of this paper. In the second chapter, we prove a conjecture about the congruence relation of generalized Frobenius-6 coloring partition function (6fnc module 243) proposed by Professor Baruah and Sarmah by means of the generating function of 6fnc (10) (given by Hirschhorn), and by using block formula and q-series operation. On this basis, we also establish some new congruence relations for the higher power of the generalized Frobenius-6 coloring partition function (6fnc module 3). In chapter 3, by using the algebraic combination method and q-series operations, we prove a large number of congruence relations on the higher power of the nW) (module 2 and 3 of the conditional Binary partition function of Ramanujan type, thus solving an open problem put forward by professors Lan and Sellers. In chapter 4, we first establish the generating function of (?) (5n) by using the computer algebra method and the identity of theta function, then we establish some new infinite family congruence relations about the Overpartitions partition function (?) (n) (module 5 and 9) by using the quadratic residue theory. The conclusions given by Treneer, Chenan Sunn Wang and Zhang are generalized.
【學位授予單位】:江蘇大學
【學位級別】:碩士
【學位授予年份】:2017
【分類號】:O157
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