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  1. No Access

    Article

    On the Irregularity of \(\pi \) -Permutation Graphs, Fibonacci Cubes, and Trees

    The irregularity of a graph G is the sum of \(|\mathrm{deg}(u) - \mathrm{deg}(v)|\) | deg ( u ) - deg ( v ) | over all edges uv of G. In this paper, this invariant is considered on \(\pi \) π -permutatio...

    Yaser Alizadeh, Emeric Deutsch… in Bulletin of the Malaysian Mathematical Sci… (2020)

  2. No Access

    Article

    M-polynomial revisited: Bethe cacti and an extension of Gutman’s approach

    The M-polynomial of a graph G is defined as \(\sum _{i\le j} m_{i,j}(G)x^iy^j\) ...

    Emeric Deutsch, Sandi Klavžar in Journal of Applied Mathematics and Computing (2019)

  3. No Access

    Article

    Adjacent q-Cycles in Permutations

    We introduce a new permutation statistic, namely, the number of cycles of length q consisting of consecutive integers, and consider the distribution of this statistic among the permutations of {1, 2, . . . , n}. ...

    Richard A. Brualdi, Emeric Deutsch in Annals of Combinatorics (2012)

  4. No Access

    Article

    Restricted Simsun Permutations

    A permutation is simsun if for all k, the subword of the one-line notation consisting of the k smallest entries does not have three consecutive decreasing elements. Simsun permutations were introduced by Simion a...

    Emeric Deutsch, Sergi Elizalde in Annals of Combinatorics (2012)

  5. No Access

    Article

    Production Matrices and Riordan Arrays

    We translate the concept of succession rule and the ECO method into matrix notation, introducing the concept of production matrix. This allows us to combine our method with other enumeration techniques using matr...

    Emeric Deutsch, Luca Ferrari, Simone Rinaldi in Annals of Combinatorics (2009)

  6. No Access

    Article

    A Simple and Unusual Bijection for Dyck Paths and its Consequences

    In this paper we introduce a new bijection from the set of Dyck paths to itself. This bijection has the property that it maps statistics that appeared recently in the study of patternavoiding permutations into...

    Sergi Elizalde, Emeric Deutsch in Annals of Combinatorics (2003)

  7. No Access

    Chapter and Conference Paper

    New Statistics on Non-crossing Trees

    A non-crossing tree is a tree drawn on the plane having as vertices a set of points on the boundary of a circle, and whose edges are straight line segments and do not cross. Continuing previous research on non...

    Emeric Deutsch, Marc Noy in Formal Power Series and Algebraic Combinatorics (2000)

  8. No Access

    Article

    On the centre of flexure

    Dans une publication publiée en 1950,Berman a déterminé les coordonnées du centre de flexion d'une barre prismatique lorsqu'on connaît seulement les valeurs de la fonction de torsion sur le contour.

    Emeric Deutsch in Zeitschrift für angewandte Mathematik und Physik ZAMP (1961)