TY - JOUR

T1 - Two-color partitions and overpartitions: a combinatorial proof

AU - Bugleev, Anton

PY - 2026/4/1

Y1 - 2026/4/1

N2 - George Andrews and Mohamed El Bachraoui recently explored identities for two-color partitions (Andrews and Bachraoui (2024) On two-color partitions with odd smallest part). In particular, they studied the connection between two-colored partitions and overpartitions. Their proofs were analytical, but they also conjectured combinatorial proofs of their results. In this paper we use two-modular diagrams to give a combinatorial proof of their main result.

AB - George Andrews and Mohamed El Bachraoui recently explored identities for two-color partitions (Andrews and Bachraoui (2024) On two-color partitions with odd smallest part). In particular, they studied the connection between two-colored partitions and overpartitions. Their proofs were analytical, but they also conjectured combinatorial proofs of their results. In this paper we use two-modular diagrams to give a combinatorial proof of their main result.

KW - Integer partitions

UR - https://www.mendeley.com/catalogue/b7ba0342-4ca0-3baf-b2eb-56d3b6800ba1/

U2 - 10.1007/s11139-026-01360-2

DO - 10.1007/s11139-026-01360-2

M3 - Article

VL - 69

JO - Ramanujan Journal

JF - Ramanujan Journal

SN - 1382-4090

IS - 4

M1 - 101

ER -