Arithmetic of partition functions and q-combinatorics

Partitions;Partition congruences;q-series;Modular forms;Combinatorial proof;Mock theta functions

Kim, Byung Chan

关键词: Partitions;    Partition congruences;    q-series;    Modular forms;    Combinatorial proof;    Mock theta functions;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/15588/Kim_ByungChang.pdf?sequence=5&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

Integer partitions play important roles in diverse areas of mathematics such as q-series, the theory of modular forms, representation theory, symmetric functions and mathematical physics. Among these, we study the arithmetic of partition functions and q-combinatorics via bijective methods, q-series and modular forms. In particular, regarding arithmetic properties of partition functions, we examine partition congruences of the overpartition function and cubic partition function and inequalities involving t-core partitions. Concerning q-combinatorics, we establish various combinatorial proofs for q-series identities appearing in Ramanujan's lost notebook and give combinatorial interpretations for third and sixth order mock theta functions.