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Supersymmetry and Combinatorics

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Abstract

We show how a recently proposed supersymmetric quantum mechanics model leads to non-trivial results/conjectures on the combinatorics of binary necklaces and linear-feedback shift-registers. Pauli’s exclusion principle plays a crucial role: by projecting out certain states/necklaces, it allows to represent the supersymmetry algebra in the resulting subspace. Some of our results can be rephrased in terms of generalizations of the well-known Witten index.

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References

  1. Veneziano G. and Wosiek J. (2006). Planar Quantum Mechanics: an Intriguing Supersymmetric example. JHEP 0601: 156

    Article  ADS  Google Scholar 

  2. Veneziano, G., Wosiek, J.: Large-N, Supersymmetry... and QCD, in Sense of Beauty in Physics - A volume in honour of Adriano Di Giacomo. Edited by M. D’Elia, K. Konishi, E. Meggiolaro, P. Rossi, Pisa Ed. PLUS, Pisa University Press, 2006

  3. Veneziano G. and Wosiek J. (2006). A supersymmetric matrix model: II. Exploring higher fermion-number sectors. JHEP 0610: 033

    Google Scholar 

  4. ’t Hooft, G.: A Planar Diagram Theory For Strong Interactions. Nucl. Phys. B72, 461 (1974); see also Veneziano, G.: Some Aspects Of A Unified Approach To Gauge, Dual And Gribov Theories. Nucl. Phys. B117, 519 (1976)

  5. Veneziano G. and Wosiek J. (2006). A supersymmetric matrix model: III. Hidden SUSY in statistical systems. JHEP 0611: 030

    Google Scholar 

  6. Beisert, N., Bianchi, M., Morales, J.F., Samtleben, H.: On the spectrum of AdS/CFT beyond supergravity. JHEP 0402, 001 (2004) and references therein

    Google Scholar 

  7. Witten, E.: Nucl. Phys. B185, 513 (1981); ibid. B202, 253 (1983)

  8. van Lint, J.H., Wilson, R.M.: A Course in combinatorics. Cambridge: Cambridge U.P., 1992

    MATH  Google Scholar 

  9. Stanley, R.P.: Enumerative combinatorics, Vol. 2, Cambridge: Cambridge U.P., 1999

    Google Scholar 

  10. Lidl, R., Niederreiter, H.: Introduction to finite fields and their applications. New York: Cambridge U.P., 1968

    Google Scholar 

  11. Sloane, N.J.A.: On-line encyclopedia of integer sequences. http://www.research.att.com/~njas

  12. Conway, J.H., Guy, R.K.: The book of numbers. N.Y.: Springer-Verlag, 1996

    MATH  Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Fisica, Università di Parma, Parma, Italy

    E. Onofri

  2. I.N.F.N., Gruppo Collegato di Parma, 43100, Parma, Italy

    E. Onofri

  3. Theory Division, CERN, CH-1211, Geneva 23, Switzerland

    G. Veneziano

  4. Collège de France, 11 place M. Berthelot, 75005, Paris, France

    G. Veneziano

  5. M. Smoluchowski Institute of Physics, Jagellonian University, Reymonta 4, 30-059, Cracow, Poland

    J. Wosiek

Authors
  1. E. Onofri
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  2. G. Veneziano
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  3. J. Wosiek
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Correspondence to G. Veneziano.

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Communicated by N.A. Nekrasov

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Onofri, E., Veneziano, G. & Wosiek, J. Supersymmetry and Combinatorics. Commun. Math. Phys. 274, 343–355 (2007). https://doi.org/10.1007/s00220-007-0281-8

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  • DOI: https://doi.org/10.1007/s00220-007-0281-8

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