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In this work, we propose a permutation invariant language model, SymphonyNet, as a solution for symbolic symphony music generation. We propose a novel Multi-track Multi-instrument Repeatable (MMR) representation for symphonic music and model the music sequence using a Transformer-based auto-regressive language model with specific 3-D positional embedding. To overcome length overflow when modeling extra-long symphony tokens, we also propose a modified Byte Pair Encoding algorithm (Music BPE) for music tokens and introduce a novel linear transformer decoder architecture as a backbone. Meanwhile, we train the decoder to learn automatic orchestration as a joint task by masking instrument information from the input. We also introduce a large-scale symbolic symphony dataset for the advance of symphony generation research. Empirical results show that the proposed approach can generate coherent, novel, complex and harmonious symphony as a pioneer solution for multi-track multi-instrument symbolic music generation.