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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Log concave sequences of symmetric functions and analogs of the Jacobi-Trudi determinants


Author: Bruce E. Sagan
Journal: Trans. Amer. Math. Soc. 329 (1992), 795-811
MSC: Primary 05E10; Secondary 05A20, 05A30, 11B65
MathSciNet review: 1066448
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Abstract: We prove that various sequences of elementary and complete homogeneous symmetric functions are log concave or PF. As corollaries we show that certain sequences of $ q$-binomial coefficients and $ q$-Stirling numbers have these properties. The principal technique used is a combinatorial interpretation of determinants using lattice paths due to Gessel and Viennot [G-V 85].


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1992-1066448-X
PII: S 0002-9947(1992)1066448-X
Keywords: Log concave, $ q$-analog, $ q$-binomial coefficients, $ q$-Stirling numbers, symmetric function, Jacobi-Trudi determinants, Gessel-Viennot lattice paths
Article copyright: © Copyright 1992 American Mathematical Society