Mediterranean Journal of Mathematics

, Volume 11, Issue 2, pp 255–271 | Cite as

Some Results on a Class of Polynomials Related to Convolutions of the Catalan Sequence

  • Stefano Capparelli
  • Paolo Maroscia


Motivated by the search of the singular values of Jordan blocks, in a previous paper (Capparelli and Maroscia in Med J Math 10:1609–1630, 2013) we studied, among other things, a family of monic polynomials with integer coefficients that turned out to be linked to convolutions of the sequence of Catalan numbers. In the present paper, we continue the study of these polynomials and prove, in particular, the irreducibility of an infinite subset of them. As an interesting byproduct, we also obtain a simple rational function in two variables which can be naturally thought of as the generating function of the Catalan number sequence and all its convolutions.

Mathematics Subject Classification (2010)

Primary 11C08 Secondary 11R09 


Irreducibility Newton’s polygon Dumas’ theorem Catalan numbers ballot numbers Bezoutian matrix Hankel matrix 


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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Dipartimento di Scienze di Base e Applicate per l’IngegneriaUniversità di Roma “La Sapienza”RomeItaly

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