The Miracle of Integer Eigenvalues

Richard Kenyon; Maxim Kontsevich; Oleg Ogievetskii; Cosmin Pohoata; Will Sawin; Semen Shlosman

doi:10.1134/S0016266324020072

The Miracle of Integer Eigenvalues

Richard Kenyon, Maxim Kontsevich, Oleg Ogievetskii, Cosmin Pohoata, Will Sawin, Semen Shlosman

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Abstract: For partially ordered sets, we consider the square matrices with rows and columns indexed by linear extensions of the partial order on. Each entry is a formal variable defined by a pedestal of the linear order with respect to linear order. We show that all eigenvalues of any such matrix are -linear combinations of those variables.

Original language	English (US)
Pages (from-to)	182-194
Number of pages	13
Journal	Functional Analysis and Its Applications
Volume	58
Issue number	2
DOIs	https://doi.org/10.1134/S0016266324020072
State	Published - Jun 2024

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

Keywords

05E10
Young diagram
filter
partially ordered set (poset)
pedestal

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10.1134/S0016266324020072

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abstract = "Abstract: For partially ordered sets, we consider the square matrices with rows and columns indexed by linear extensions of the partial order on. Each entry is a formal variable defined by a pedestal of the linear order with respect to linear order. We show that all eigenvalues of any such matrix are -linear combinations of those variables.",

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author = "Richard Kenyon and Maxim Kontsevich and Oleg Ogievetskii and Cosmin Pohoata and Will Sawin and Semen Shlosman",

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AU - Kenyon, Richard

AU - Kontsevich, Maxim

AU - Ogievetskii, Oleg

AU - Pohoata, Cosmin

AU - Sawin, Will

AU - Shlosman, Semen

N1 - Publisher Copyright: © Pleiades Publishing, Ltd. 2024.

PY - 2024/6

Y1 - 2024/6

N2 - Abstract: For partially ordered sets, we consider the square matrices with rows and columns indexed by linear extensions of the partial order on. Each entry is a formal variable defined by a pedestal of the linear order with respect to linear order. We show that all eigenvalues of any such matrix are -linear combinations of those variables.

AB - Abstract: For partially ordered sets, we consider the square matrices with rows and columns indexed by linear extensions of the partial order on. Each entry is a formal variable defined by a pedestal of the linear order with respect to linear order. We show that all eigenvalues of any such matrix are -linear combinations of those variables.

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KW - Young diagram

KW - filter

KW - partially ordered set (poset)

KW - pedestal

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JF - Functional Analysis and Its Applications

IS - 2

ER -

The Miracle of Integer Eigenvalues

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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