Duke Mathematical Journal

A combinatorial description of the spectrum for the Tsetlin library and its generalization to hyperplane arrangements

Pat Bidigare, Phil Hanlon, and Dan Rockmore

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Article information

Duke Math. J. Volume 99, Number 1 (1999), 135-174.

First available in Project Euclid: 19 February 2004

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 52C35: Arrangements of points, flats, hyperplanes [See also 32S22]
Secondary: 15A18: Eigenvalues, singular values, and eigenvectors


Bidigare, Pat; Hanlon, Phil; Rockmore, Dan. A combinatorial description of the spectrum for the Tsetlin library and its generalization to hyperplane arrangements. Duke Math. J. 99 (1999), no. 1, 135--174. doi:10.1215/S0012-7094-99-09906-4. http://projecteuclid.org/euclid.dmj/1077227634.

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  • [BaD] Dave Bayer and Persi Diaconis, Trailing the dovetail shuffle to its lair, Ann. Appl. Probab. 2 (1992), no. 2, 294–313.
  • [BrD] K. Brown and P. Diaconis, Random walk and hyperplane arrangements, to appear.
  • [D1] Persi Diaconis, Group representations in probability and statistics, Institute of Mathematical Statistics Lecture Notes—Monograph Series, 11, Institute of Mathematical Statistics, Hayward, CA, 1988.
  • [D2] Persi Diaconis, The cutoff phenomenon in finite Markov chains, Proc. Nat. Acad. Sci. U.S.A. 93 (1996), no. 4, 1659–1664.
  • [DFP] Persi Diaconis, James Allen Fill, and Jim Pitman, Analysis of top to random shuffles, Combin. Probab. Comput. 1 (1992), no. 2, 135–155.
  • [DMP] Persi Diaconis, Michael McGrath, and Jim Pitman, Riffle shuffles, cycles, and descents, Combinatorica 15 (1995), no. 1, 11–29.
  • [Do] Peter Donnelly, The heaps process, libraries, and size-biased permutations, J. Appl. Probab. 28 (1991), no. 2, 321–335.
  • [F] James Allen Fill, An exact formula for the move-to-front rule for self-organizing lists, J. Theoret. Probab. 9 (1996), no. 1, 113–160.
  • [FHo] James Allen Fill and Lars Holst, On the distribution of search cost for the move-to-front rule, Random Structures Algorithms 8 (1996), no. 3, 179–186.
  • [H] Phil Hanlon, The action of $S\sb n$ on the components of the Hodge decomposition of Hochschild homology, Michigan Math. J. 37 (1990), no. 1, 105–124.
  • [KR] Sanjiv Kapoor and Edward M. Reingold, Stochastic rearrangement rules for self-organizing data structures, Algorithmica 6 (1991), no. 2, 278–291.
  • [OT] Peter Orlik and Hiroaki Terao, Arrangements of hyperplanes, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 300, Springer-Verlag, Berlin, 1992.
  • [P] R. M. Phatarfod, On the matrix occurring in a linear search problem, J. Appl. Probab. 28 (1991), no. 2, 336–346.
  • [S] Richard P. Stanley, Enumerative combinatorics. Vol. I, The Wadsworth & Brooks/Cole Mathematics Series, Wadsworth & Brooks/Cole Advanced Books & Software, Monterey, CA, 1986.
  • [V] Alexandre Varchenko, Bilinear form of real configuration of hyperplanes, Adv. Math. 97 (1993), no. 1, 110–144.
  • [Z] Thomas Zaslavsky, Facing up to arrangements: face-count formulas for partitions of space by hyperplanes, Mem. Amer. Math. Soc. 1 (1975), no. issue 1, 154, vii+102.