Geodesic
The miracle of integer eigenvalues
Funkcionalʹnyj analiz i ego priloženiâ, Tome 58 (2024) no. 2, pp. 100-114 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: partially ordered set (poset), pedestal, filter, Young diagram. 
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Richard Kenyon; Maxim Kontsevich; Oleg Ogievetskii; Cosmin Pohoata; Will Sawin; Semen Shlosman. The miracle of integer eigenvalues. Funkcionalʹnyj analiz i ego priloženiâ, Tome 58 (2024) no. 2, pp. 100-114. http://geodesic.mathdoc.fr/item/FAA_2024_58_2_a6/

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