Richard Kenyon, Maxim Kontsevich, Oleg Ogievetskii, Cosmin Pohoata, Will Sawin, Semen Shlosman
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引用次数: 0
Abstract
For partially ordered sets \((X, \preccurlyeq)\), we consider the square matrices \(M^{X}\) with rows and columns indexed by linear extensions of the partial order on \(X\). Each entry \((M^{X})_{PQ}\) is a formal variable defined by a pedestal of the linear order \(Q\) with respect to linear order \(P\). We show that all eigenvalues of any such matrix \(M^{X}\) are \(\mathbb{Z}\)-linear combinations of those variables.
期刊介绍:
Functional Analysis and Its Applications publishes current problems of functional analysis, including representation theory, theory of abstract and functional spaces, theory of operators, spectral theory, theory of operator equations, and the theory of normed rings. The journal also covers the most important applications of functional analysis in mathematics, mechanics, and theoretical physics.