Statistical mechanics of combinatorial partitions, and their limit shapes

A. M. Vershik

doi:10.1007/bf02509449

journal article Apr 01, 1996

Statistical mechanics of combinatorial partitions, and their limit shapes

A. M. Vershik

Functional Analysis and Its Applications Vol. 30 No. 2 pp. 90-105 · Springer Science and Business Media LLC

View at Publisher Save 10.1007/bf02509449

Topics

No keywords indexed for this article. Browse by subject →

References

19

[1]

A. M. Vershik, Asymptotic Combinatorics and Algebraic Analysis, Proceedings of ICM, Vol. 2, Birkhäuser, Zurich (1995).

[2]

R. Arratia and S. Tavare, “Limit theorems for combinatorial structures,” Rand. Structure Alg.,3, 321–345 (1992). 10.1002/rsa.3240030310

[3]

B. Fristedt, “The structure of random partitions of large integers,” Trans. Am. Math. Soc.,337, 703–735 (1993). 10.2307/2154239

[4]

J. Pimtan and R. Aldous, “Brownian bridge asymptotics for random mappings,” Rand. Structure Alg.,5, 487–512 (1994). 10.1002/rsa.3240050402

[5]

K. Huang, Statistical Mechanics, John Wiley & Sons, New York-London (1963).

[6]

A. Ya. Khinchin, Mathematical Foundations of Quantum Statistics [in Russian], Fizmatlit, Moscow-Leningrad (1951).

[7]

G. Freiman, New Analytical Results in Subset-Sum Problems, Combinatorics and Algorithms, Jerusalem (1988).

[8]

A. M. Vershik, “The limit form of convex integral polygons and related questions,” Funkts. Anal. Prilozhen.,28, No. 1, 17–25 (1994).

[9]

I. Barany, “The limit shape of convex lattice polygons,” Discrete Comput. Geom.,13, 279–295 (1995). 10.1007/bf02574045

[10]

Ya. G. Sinai, “A probabilistic approach to the analysis of the statistics of convex polygonal lines,” Funkts. Anal. Prilozhen.,28, No. 2, 41–48 (1994).

[11]

A. M. Vershik, “Statistics of the set of naturals partitions,” in: Probab. Theory Math. Stat., Vol. 2, 683–694, VNU Sci. Press.

[12]

Yu. Yakubovich, “Asymptotics of random partitions of a set,” Zap. Nauchm. Semin. POMI,223, 227–250 (1995).

[13]

G. E. Andrews, The Theory of Partitions, Addison Wesley, London-Amsterdam (1976).

[14]

C. L. Siegel, Lecture on Advanced Analytic Number Theory, Tata Inst., Bombay (1961).

[15]

M. Szalay and R. Turan, “On some problems of statistical theory of partitions. I,” Acta Math. Acad. Sci. Hungr.,29, 361–379 (1977). 10.1007/bf01895857

[16]

A. M. Vershik and S. V. Kerov, “Asymptotics of maximal and typical dimensionality of irreducible partitions of the symmetric group,” Funkts. Anal. Prilozhen.,19, No. 1, 25–36 (1985).

[17]

I. M. Ryzhik and I. S. Gradstein, Tables of Integrals, Sums, Series, and Products [in Russian], 4th ed., Fizmatlit, Moscow (1963).

[18]

A. M. Vershik and A. A. Shmidt, “Limit measures arising in the asymptotic theory of symmetric groups,” Teor. Verovatn. Primenen.,22, No. 1, 72–88 (1978);23, No. 1, 42–54 (1979).

[19]

A. M. Vershik, “Statistical sum related to Young diagrams,” Zap. Nauchn. Sem. LOMI,164, 20–29 (1987); English transl. in J. Soviet Math.,47, 2379–2386 (1989).

Cited By

168

Set partitions and integrable hierarchies

V. É. Adler · 2016

Theoretical and Mathematical Physic...

Metrics

168

Citations

19

References

Details

Published: Apr 01, 1996
Vol/Issue: 30(2)
Pages: 90-105
License: View

Authors

A

A. M. Vershik

Cite This Article

A. M. Vershik (1996). Statistical mechanics of combinatorial partitions, and their limit shapes. Functional Analysis and Its Applications, 30(2), 90-105. https://doi.org/10.1007/bf02509449

Statistical mechanics of combinatorial partitions, and their limit shapes

You May Also Like