Abstract
We consider the family of nearest neighbour interacting particle systems on Z allowing 0, 1 or 2 particles at a site. We parametrize a wide subfamily of processes exhibiting product blocking measure and show how this family can be "stood up" in the sense of Balazs and Bowen. By comparing measures we prove new three variable Jacobi style identities, related to counting certain generalised Frobenius partitions with a 2-repetition condition. By specialising to specific processes we produce two variable identities that are shown to relate to Jacobi triple product and various other identities of combinatorial significance. The family of k-exclusion processes for arbitrary k are also considered and are shown to give similar Jacobi style identities relating to counting generalised Frobenius partitions with a k-repetition condition.
Original language | English |
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Article number | 48 |
Number of pages | 39 |
Journal | Research in the Mathematical Sciences |
Volume | 9 |
Issue number | 3 |
DOIs | |
Publication status | Published - 21 Jul 2022 |
Bibliographical note
Funding Information:The authors are grateful for discussions with János Engländer regarding the parity of the sum of Bernoulli random variables and for suggestions of an anonymous referee regarding the combinatorial background of our identities. M. Balázs was partially supported by the EPSRC EP/R021449/1 Standard Grant of the UK. On behalf of all authors, the corresponding author states that there is no conflict of interest and that there are no associated data for this manuscript.
Publisher Copyright:
© 2022, The Author(s).