Basic hypergeometric summations from rook theory
Michael J. Schlosser, Meesue Yoo
TL;DR
This paper uses an extended q-rook theory to provide combinatorial proofs for important basic hypergeometric summations, enhancing understanding of their combinatorial structure.
Contribution
It introduces a one-variable extension of q-rook theory to prove key hypergeometric summations combinatorially, offering new insights into their structure.
Findings
Provided combinatorial proofs for q-Pfaff-Saalschütz summation
Proved a 4phi3 summation by Jain using rook theory
Extended q-rook theory to a one-variable case
Abstract
We employ a one-variable extension of q-rook theory to give combinatorial proofs of some basic hypergeometric summations, including the q-Pfaff-Saalsch\"utz summation and a 4phi3 summation by Jain.
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