Liuquan Wang

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20222026

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math.CO2026

Proofs of four Takigiku--Tsuchioka conjectures on level $2$ principal characters of $A_{2 ℓ - 1}^{(2)}$

Liuquan Wang

We prove four conjectures of Takigiku and Tsuchioka consisting of eight Rogers--Ramanujan type identities. Two conjectures involve triple sums and a third involves quadruple sums,…

math.CO2026

Proofs of Some Kanade--Russell Mod 12 Conjectures

Liuquan Wang

Kanade and Russell conjectured seventeen Rogers--Ramanujan type identities of modulus 12. Eleven of these identities involving triple sums were proved by Bringmann--Jennings-Shaffe…

math.CO2025

Nahm sum identities for Cartan matrices of type $D_{k}$

Liuquan Wang, Shangwen Wang

Around 2007, Warnaar proved four identities related to Nahm sums associated with twice the inverse of the Cartan matrix of type $D_{k}$ . Three of these had been conjectured by Flohr,…

Proofs of four Takigiku--Tsuchioka conjectures on level 2 principal characters of A2ℓ−1(2)​

Proofs of Some Kanade--Russell Mod 12 Conjectures

Nahm sum identities for Cartan matrices of type Dk​

Proofs of four Takigiku--Tsuchioka conjectures on level $2$ principal characters of $A_{2 ℓ - 1}^{(2)}$

Nahm sum identities for Cartan matrices of type $D_{k}$