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We give probabilistic proofs to well-known combinatorial identities; theDurfee rectangles identity, Euler's identity and the $q$-Binomial Theorem. Weuse the asymmetric simple exclusion process on $\mathbb{Z}$ under its naturalproduct blocking measure to achieve this. The results we derive also allow usto determine the stationary distribution of second class particles in theblocking scenario.

ASEP proofs of some partition identities and the blocking stationary behaviour of second class particles