An extension to overpartitions of Rogers-Ramanujan identities for even moduli

Autor: Sylvie Corteel, Jeremy Lovejoy, Olivier Mallet

Publikováno v: Discrete Mathematics & Theoretical Computer Science, Vol DMTCS Proceedings vol. AG,..., Iss Proceedings (2006)

We investigate class of well-poised basic hypergeometric series $\tilde{J}_{k,i}(a;x;q)$, interpreting these series as generating functions for overpartitions defined by multiplicity conditions. We also show how to interpret the $\tilde{J}_{k,i}(a;1;

Externí odkaz: https://doaj.org/article/92e3d80e0c9f4068bec454c091e3f167

Bailey pairs and indefinite quadratic forms, II. False indefinite theta functions

Autor: Jeremy Lovejoy

Publikováno v: Research in Number Theory. 8

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::01172c8049a32bb8c9708dc14fde97f8
https://doi.org/10.1007/s40993-022-00324-x

The colored Jones polynomial and Kontsevich–Zagier series for double twist knots

Autor: Jeremy Lovejoy, Robert Osburn

Publikováno v: Journal of Knot Theory and Its Ramifications
Journal of Knot Theory and Its Ramifications, World Scientific Publishing, 2021, 30 (05), pp.2150031. ⟨10.1142/S0218216521500310⟩

International audience; Using a result of Takata, we prove a formula for the colored Jones polynomial of the double twist knots [Formula: see text] and [Formula: see text] where [Formula: see text] and [Formula: see text] are positive integers. In th

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c63e5e30f0e4c79f0c233114535cf5ad
https://hal.archives-ouvertes.fr/hal-03382638

Parity bias in partitions

Autor: Eunmi Kim, Byungchan Kim, Jeremy Lovejoy

Publikováno v: European Journal of Combinatorics
European Journal of Combinatorics, Elsevier, 2020, 89, pp.103159. ⟨10.1016/j.ejc.2020.103159⟩

Let p o ( n ) denote the number of partitions of n with more odd parts than even parts and let p e ( n ) denote the number of partitions of n with more even parts than odd parts. Using q -series transformations we find a generating function for p o (

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::dbabcaf562ccbc40ce5ec0f7738d6d21
https://hal.archives-ouvertes.fr/hal-03382657

Ramanujan-type partial theta identities and conjugate Bailey pairs, II. Multisums

Autor: Jeremy Lovejoy, Byungchan Kim

Publikováno v: The Ramanujan Journal. 46:743-764

In the first paper of this series, we described how to find conjugate Bailey pairs from residual identities of Ramanujan-type partial theta identities. Here we carry this out for four multisum residual identities of Warnaar and two more due to the au

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::ef4ffc40d94bdb05084b1e1b9e96e234
https://doi.org/10.1007/s11139-017-9919-0