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Some Conjectures for Immanants

Published online by Cambridge University Press:  20 November 2018

J. R. Stembridge
J. R. Stembridge*
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, Michigan, U.S.A. 48109-1003
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Abstract

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We present a series of conjectures for immanants, together with the supporting evidence we possess for them. The conjectures are loosely organized into three families. The first concerns inequalities involving the immanants of totally positive matrices (Le.,real matrices with nonnegative minors). This includes, for example, the conjecture that immanants of totally positive matrices are nonnegative. The second family involves the immanants of Jacobi-Trudi matrices. These conjectures were suggested by a previous conjecture of Goulden and Jackson (recently proved by C. Greene) that the immanants of Jacobi-Trudi matrices are polynomials with nonnegative coefficients. The third family involves geometric and combinatorial structures associated with total positivity and paths in acyclic digraphs.

Keywords

15A1505E0520C3015A45
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 44 , Issue 5 , 01 October 1992 , pp. 1079 - 1099
Copyright
Copyright © Canadian Mathematical Society 1992

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