The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on November 8, 2022 at 1:30 pm (UTC+3) in Room 478 of IMI.
A talk on:
Surfaces Associated with Pascal and Catalan Triangles
will be delivered by Leonard DAUS1, Marilena JIANU1 and Adela MIHAI1,2
1 Technical University of Civil Engineering Bucharest, Romania
2 Transilvania University of Brasov, Romania.
Everybody is invited.
Abstract. An open problem in reliability theory is that of finding all the coefficients of the reliability polynomial associated with particular networks. Because reliability polynomials can be expressed in Bernstein form (hence linked to binomial coefficients), it is clear that an extension of the classical discrete Pascal’s triangle (comprising all the binomial coefficients) to a continuous version (exhibiting infinitely many values in between the binomial coefficients) might be geometrically helpful and revealing [1]. We investigated in [2] some geometric properties of a continuous extension of Pascal’s triangle: Gauss curvature, mean curvature, geodesics and level curves, as well as their symmetries. As a next step [3], we investigate a surface related to one of the Catalan triangles presented in [4].
References:
[1] M. Jianu, L. Daus, M. Nagy, R.M. Beiu, Approximating the level curves on Pascal’s surface, International Journal of Computers, Communications & Control 17(4) (2022), art. 4865.
[2] V. Beiu, L. Daus, M. Jianu, A. Mihai, I. Mihai, On a surface associated with Pascal’s triangle, Symmetry 14(2) (2022), art. 411.
[3] M. Jianu, S. Achimescu, L. Daus, I. Mierlus-Mazilu, A. Mihai, D. Tudor, On a surface associated to Catalan triangle, submitted.
[4] L. Daus, M. Jianu, R.M. Beiu, V. Beiu, A tale of Catalan triangles – counting lattice paths, 9th International Workshop on Soft Computing Applications – SOFA 2020, 27-29 November 2020, Arad, Romania.
Funding: Work supported by the research project SUPREMA UTCB-CDI-2022-008 of the Technical University of Civil Engineering Bucharest.