Skip to main content

Conjugation properties in incidence algebras


Incidence algebras can be regarded as a generalization of full matrix algebras. We present some conjugation properties for incidence functions. The list of results is as follows: a criterion for a convexdiagonal function f to be conjugated to the diagonal function fe; conditions under which the conjugacy fCe + ζ -holds (the function Ce + ζ -may be thought of as an analog for a Jordan box from matrix theory); a proof of the conjugation of two functions ζ < and gz -for partially ordered sets that satisfy the conditions mentioned above; an example of a partially ordered set for which the conjugacy ζ <ζ -does not hold. These results involve conjugation criteria for convex-diagonal functions of some partially ordered sets.

This is a preview of subscription content, access via your institution.


  1. 1.

    M. Aigner, Combinatorial Theory, Grundlehren Math. Wiss., Vol. 234, Springer, Berlin (1979).

    Google Scholar 

  2. 2.

    P. Doubilet, G.-C. Rota, and R. Stanley, “On the foundations of combinatorial theory (VI): The idea of generating function,” in: Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Vol. II, University of California Press (1972), pp. 267–318.

    MathSciNet  Google Scholar 

  3. 3.

    V. Marenich, “Conjugation properties of incidence functions,” Proc. of the VII Int. Conf. on Discrete Mathematics and Its Applications, Part 3, MSU, Moscow (2001), pp. 384–386.

    Google Scholar 

  4. 4.

    K. A. Rybnikov, Introduction to Combinatorial Analysis [in Russian], Izd. Mosk. Univ., Moscow (1985).

    Google Scholar 

  5. 5.

    E. Spiegel and C. J. O’Donnell, Incidence Algebras, Marcel Dekker, New York (1997).

    Google Scholar 

  6. 6.

    R. P. Stanley, Enumerative Combinatorics, Vol. 1, Wadsworth (1986).

Download references

Author information



Additional information


Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 3, pp. 111–123, 2003.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Marenich, V.E. Conjugation properties in incidence algebras. J Math Sci 135, 3341–3349 (2006).

Download citation


  • Matrix Theory
  • Matrix Algebra
  • Full Matrix
  • Diagonal Function
  • Full Matrix Algebra