On a pair of three-colored (mod 10) partition identities
2025/09/08 by Russell, Matthew C.
#05A17 #11P84 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2509.07169
Abstract
We prove a pair of (mod 10) partition identities. The sum sides involve three-colored partitions into distinct parts, while the product sides are the generating functions for distinct partitions times the Rogers-Ramanujan products. Our proofs make heavy use of Maple to verify that functional equations are satisfied.
Citations
- Some New Modular Rank Four Nahm Sums as Lift-dual of Rank Three Examples
- Proofs of Two Conjectural Identities on Partial Nahm Sums
- Proofs of Mizuno's Conjectures on Rank Three Nahm Sums of Index (1,2,2)
- A refinement of and a companion to MacMahon's partition identity
- Rogers-Ramanujan type identities involving double, triple and quadruple sums
- On Some Double Nahm Sums of Zagier
- Principal subspaces of basic modules for twisted affine Lie algebras, q-series multisums, and Nandi's identities
- A proof of conjectured partition identities of Nandi
- Linked partition ideals, directed graphs and q-multi-summations
- On partition identities of Capparelli and Primc
- On a Rogers-Ramanujan type identity from crystal base theory
- Unification, refinements and companions of generalisations of Schur's\n theorem
- Siladić's theorem: weighted words, refinement and companion
- IdentityFinder and some new identities of Rogers-Ramanujan type
- Twisted \mathfraksl(3,\C)\sptilde-modules and combinatorial identities
- Annihilating fields of standard modules of sl(2,C)~ and combinatorial identities
Related