On q-integrals over order polytopes

Jang Soo Kim, Dennis Stanton

Research output: Contribution to journalConference articlepeer-review


A q-integral over an order polytope coming from a poset is interpreted as a generating function of linear extensions of the poset. As an application, the q-beta integral and a q-analog of Dirichlet's integral are computed. A combinatorial interpretation of a q-Selberg integral is also obtained.

Original languageEnglish (US)
Pages (from-to)707-718
Number of pages12
JournalDiscrete Mathematics and Theoretical Computer Science
StatePublished - 2016
Event28th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2016 - Vancouver, Canada
Duration: Jul 4 2016Jul 8 2016

Bibliographical note

Funding Information:
†The first author was partially supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2013R1A1A2061006). ‡The second author was supported by NSF grant DMS-1148634.

Publisher Copyright:
© 2016 Discrete Mathematics and Theoretical Computer Science (DMTCS), Nancy, France to reconstruct the historical associations between the phylogenies of host and parasite under a model of parasites switching hosts, which is an instance of the more general problem of cophylogeny estimation.


  • Order polytope
  • Q-Selberg integral
  • Q-integral


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