Properties of triangular partitions and their generalizations

• Autores: Alejandro B. Galván
• Localización: Reports@SCM: an electronic journal of the Societat Catalana de Matemàtiques, ISSN-e 2385-4227, Vol. 9, Nº. 1, 2024, págs. 31-40
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen
  • català

    Una partició entera es diu triangular si el seu diagrama de Ferrers es pot separar del seu complement (com a subconjunt de N2) amb una línia recta. Aquest article es basa en alguns desenvolupaments recents sobre el tema per derivar noves propietats enumeratives, geomètriques i algorísmiques d’aquests objectes. La investigació s’estén després a generalitzacions en dimensions superiors, anomenades particions piramidals, i a particions convexes i còncaves, definides com particions amb un diagrama de Ferrers que pot ser separat del seu complement per una corba convexa o còncava.

  • English

    An integer partition is said to be triangular if its Ferrers diagram can be separated from its complement (as a subset of N2) by a straight line. This article builds on some recent developments on the topic in order to derive new enumerative, geometric and algorithmic properties of these objects. The research is then extended to higher-dimensional generalizations, called pyramidal partitions, and to convex and concave partitions, defined as partitions whose Ferrers diagram can be separated from its complement by a convex or concave curve.

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