Rejoinder on: Recent progress on the combinatorial diameter of polytopes and simplicial complexes

• Francisco Santos ^[1]
  1. [1] Universidad de Cantabria

     Universidad de Cantabria

     Santander, España

     
• Localización: Top, ISSN-e 1863-8279, ISSN 1134-5764, Vol. 21, Nº. 3, 2013, págs. 482-484
• Idioma: inglés
• DOI: 10.1007/s11750-013-0296-6
• Enlaces
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• Resumen

  • Hiriart–Urruty reminds us of something I completely agree; in order to advance forward we need to look at the past and understand what others did. In this respect, let me mention that (as is hinted in Sect. 4.2) my counterexamples to the (bounded) Hirsch conjecture (F. Santos 2012) use two ideas from the 45-year old paper by Klee and Walkup (1967). (Unless otherwise stated, all references in this rejoinder refer to the bibliography in the main paper). On the one hand, the Strong d-step Lemma (Theorem 4.8) is an extension of the original d-step lemma of Klee and Walkup (Lemma 4.7).