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Kirillov's Unimodality Conjecture for the Rectangular Narayana Polynomials

Herman Z. Q. Chen, Arthur L. B. Yang, Philip B. Zhang
2018 Electronic Journal of Combinatorics  
In the study of Kostka numbers and Catalan numbers, Kirillov posed a unimodality conjecture for the rectangular Narayana polynomials.  ...  We prove that the rectangular Narayana polynomials have only real zeros, and thereby confirm Kirillov's unimodality conjecture.  ...  Acknowledgements We would like to thank the anonymous referee for the valuable comments.  ... 
doi:10.37236/6806 fatcat:a5e7ntvdtzfhrka2pdigspd2ru

Kirillov's unimodality conjecture for the rectangular Narayana polynomials [article]

Herman Z.Q. Chen, Arthur L.B. Yang, Philip B. Zhang
2016 arXiv   pre-print
In the study of Kostka numbers and Catalan numbers, Kirillov posed a unimodality conjecture for the rectangular Narayana polynomials.  ...  We prove that the rectangular Narayana polynomials have only real zeros, and thereby confirm Kirillov's unimodality conjecture with the help of Newton's inequality.  ...  This work was supported by the 973 Project, the PC-SIRT Project of the Ministry of Education and the National Science Foundation of China.  ... 
arXiv:1601.05863v1 fatcat:62aqsxrub5d3hghei647sdvt6u