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Compositions of n as alternating sequences of weakly increasing and strictly decreasing partitions

Aubrey Blecher, Charlotte Brennan, Toufik Mansour (2012)

Open Mathematics

Compositions and partitions of positive integers are often studied in separate frameworks where partitions are given by q-series generating functions and compositions exhibiting specific patterns are designated by generating functions for these patterns. Here, we view compositions as alternating sequences of weakly increasing and strictly decreasing partitions (i.e. alternating blocks). We obtain generating functions for the number of such partitions in terms of the size of the composition, the...

Counting biorders.

Christophe, Julie, Doignon, Jean-Paul, Fiorini, Samuel (2003)

Journal of Integer Sequences [electronic only]

Counting colorings on varieties.

Fernando Rodríguez-Villegas (2007)

Publicacions Matemàtiques

We present a combinatorial mechanism for counting certain objects associated to a variety over a finite field. The basic example is that of counting conjugacy classes of the general linear group. We discuss how the method applies to counting these and also to counting unipotent matrices and pairs of commuting matrices.[Proceedings of the Primeras Jornadas de Teoría de Números (Vilanova i la Geltrú (Barcelona), 30 June - 2 July 2005)].

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