LINKED PARTITION IDEALS AND ANDREWS–GORDON TYPE SERIES FOR ALLADI AND GORDON’S EXTENSION OF SCHUR’S IDENTITY

A BSTRACT . Based on the framework of linked partition ideals, we derive some double and triple series of Andrews–Gordon type for partitions in Alladi and Gordon’s extension of Schur’s identity. We also display similar series for such partitions with additional restrictions on the smallest part. Also, an alternative proof of Alladi and Gordon’s extension of Schur’s identity is presented.