{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/15588"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/15588","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Arithmetic of partition functions and q-combinatorics","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Kim, Byung Chan"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Berndt, Bruce C.","Ahlgren, Scott","Zaharescu, Alexandru","Yong, Alexander"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2010,"date_issued":"2010-05-14T20:51:42Z","date_published":"2010-05-14T20:51:42Z","updated_at":"2026-07-22T22:25:08Z","subjects":["Partitions","Partition congruences","q-series","Modular forms","Combinatorial proof","Mock theta functions"],"languages":["en"],"rights":["Copyright 2010 Byung Chan Kim"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/15588","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Berndt, Bruce C.","Ahlgren, Scott","Zaharescu, Alexandru","Yong, Alexander"]},{"key":"dc:creator","label":"Author","values":["Kim, Byung Chan"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2010-05-14T20:51:42Z","2012-05-15T10:00:49Z","2010-5"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Partitions","Partition congruences","q-series","Modular forms","Combinatorial proof","Mock theta functions"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2010 Byung Chan Kim"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/15588"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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.","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"]},{"key":"dc:title","label":"Title","values":["Arithmetic of partition functions and q-combinatorics"]}]}],"canonical_facts":{"dc:contributor":["Berndt, Bruce C.","Ahlgren, Scott","Zaharescu, Alexandru","Yong, Alexander"],"dc:creator":["Kim, Byung Chan"],"dc:date":["2010-05-14T20:51:42Z","2012-05-15T10:00:49Z","2010-5"],"dc:description":["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.","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"],"dc:identifier":["http://hdl.handle.net/2142/15588"],"dc:language":["en"],"dc:rights":["Copyright 2010 Byung Chan Kim"],"dc:subject":["Partitions","Partition congruences","q-series","Modular forms","Combinatorial proof","Mock theta functions"],"dc:title":["Arithmetic of partition functions and q-combinatorics"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:08Z"}