Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On realization of Björner’s “continuous partition lattice” by measurable partitions
HTML articles powered by AMS MathViewer

by Mark D. Haiman
Trans. Amer. Math. Soc. 343 (1994), 695-711
DOI: https://doi.org/10.1090/S0002-9947-1994-1211408-0

Abstract:

Björner [1] showed how a construction by von Neumann of examples of continuous geometries can be adapted to construct a continuous analogue of finite partition lattices. Björner’s construction realizes the continuous partition lattice abstractly, as a completion of a direct limit of finite lattices. Here we give an alternative construction realizing a continuous partition lattice concretely as a lattice of measurable partitions. This new lattice contains the Björner lattice and shares its key properties. Furthermore its automorphism group is the full automorphism group $\pmod 0$ of the unit interval with Lebesgue measure, whereas, as we show, the Björner lattice possesses only a proper subgroup of these automorphisms.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 06C10, 28D99
  • Retrieve articles in all journals with MSC: 06C10, 28D99
Bibliographic Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 343 (1994), 695-711
  • MSC: Primary 06C10; Secondary 28D99
  • DOI: https://doi.org/10.1090/S0002-9947-1994-1211408-0
  • MathSciNet review: 1211408