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Berndt, Bruce C. Ahlgren, Scott Zaharescu, Alexandru Yong, Alexander Berndt, Bruce C. Ahlgren, Scott Kim, Byung Chan 2010-05-14T20:51:42Z 2010-05-14T20:51:42Z 2012-05-15T10:00:49Z 2010-05-14T20:51:42Z 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lost notebook and give combinatorial interpretations for third and sixth order mock theta functions. 2010-5 Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2010-04-15T21:19:36Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 3 BYUNGCHAN_KIM.tex: 272315 bytes, checksum: e27fe09d5cb98bed16bb89d6b154ca52 (MD5) BYUNGCHAN_KIM.pdf: 575408 bytes, checksum: 0b343cf568fe00666277969e48f9887a (MD5) BYUNGCHAN_KIM.pdf: 575408 bytes, checksum: 0b343cf568fe00666277969e48f9887a (MD5) Made available in DSpace on 2010-05-14T20:51:42Z (GMT). No. of bitstreams: 7 BYUNGCHAN_KIM.tex: 272317 bytes, checksum: e94d7c03c7c07e5e96958fcd03938fd2 (MD5) BYUNGCHAN_KIM.pdf: 575435 bytes, checksum: d7297c8741b748548938ebf6f470cd88 (MD5) 1_BYUNGCHAN_KIM.pdf: 575408 bytes, checksum: 0b343cf568fe00666277969e48f9887a (MD5) 2_BYUNGCHAN_KIM.pdf: 575408 bytes, checksum: 0b343cf568fe00666277969e48f9887a (MD5) Kim_ByungChang.pdf: 575435 bytes, checksum: d7297c8741b748548938ebf6f470cd88 (MD5) thesis2.bib: 55502 bytes, checksum: 970df40db242ac0c14c045c5e2f2c96d (MD5) license.txt: 4056 bytes, checksum: 199f4c1c5eadcb0a4ec4cbc4967e6f65 (MD5) Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by William Ingram (wingram2@illinois.edu) on 2010-05-14T20:52:49Z Item is restricted until 2012-05-14T20:52:43Z Item reinstated by Sarah Shreeves (sshreeve@illinois.edu) on 2012-05-15T10:00:49Z Item was in collections: University of Illinois Dissertations and Theses (ID: 204) Dissertations and Theses - Mathematics (ID: 749) No. of bitstreams: 8 Kim_ByungChang.pdf.txt: 190021 bytes, checksum: 7e31e312517116f648709eaa04638e55 (MD5) BYUNGCHAN_KIM.tex: 272317 bytes, checksum: e94d7c03c7c07e5e96958fcd03938fd2 (MD5) BYUNGCHAN_KIM.pdf: 575435 bytes, checksum: d7297c8741b748548938ebf6f470cd88 (MD5) 1_BYUNGCHAN_KIM.pdf: 575408 bytes, checksum: 0b343cf568fe00666277969e48f9887a (MD5) 2_BYUNGCHAN_KIM.pdf: 575408 bytes, checksum: 0b343cf568fe00666277969e48f9887a (MD5) Kim_ByungChang.pdf: 575435 bytes, checksum: d7297c8741b748548938ebf6f470cd88 (MD5) thesis2.bib: 55502 bytes, checksum: 970df40db242ac0c14c045c5e2f2c96d (MD5) license.txt: 4056 bytes, checksum: 199f4c1c5eadcb0a4ec4cbc4967e6f65 (MD5) Item released from any restrictions by Sarah Shreeves (sshreeve@illinois.edu) on 2012-05-15T10:00:49Z http://hdl.handle.net/2142/15588 en Copyright 2010 Byung Chan Kim Partitions Partition congruences q-series Modular forms Combinatorial proof Mock theta functions Arithmetic of partition functions and q-combinatorics Mathematics 1257 Mathematics 0439 University of Illinois at Urbana-Champaign Dissertation Ph.D. PHD:Mathematics -UIUC 10KS0439PHD