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Two Enriched Poset Polytopes

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Abstract

Stanley introduced and studied two lattice polytopes, the order polytope and chain polytope, associated with a finite poset. Recently, Ohsugi and Tsuchiya introduce an enriched version of them, called the enriched order polytope and enriched chain polytope. In this paper, we give a piecewise-linear bijection between these enriched poset polytopes, which is an enriched analogue of Stanley’s transfer map and bijectively proves that they have the same Ehrhart polynomials. Also, we construct explicitly unimodular triangulations of two enriched poset polytopes, which are the order complexes of graded posets.

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Acknowledgements

The first author was partially supported by JSPS KAKENHI 18K03208 and the second author was partially supported by JSPS KAKENHI 19J00312, 19K14505, and 22K13890.

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Authors and Affiliations

  1. Graduate School of Mathematics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya , 464-8602, Japan

    Soichi Okada

  2. Department of Information Science, Faculty of Science, Toho University, Miyama, Funabashi-shi, Chiba , 274-8510, Japan

    Akiyoshi Tsuchiya

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  1. Soichi Okada
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  2. Akiyoshi Tsuchiya
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Correspondence to Akiyoshi Tsuchiya.

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Communicated by Éric Fusy.

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Okada, S., Tsuchiya, A. Two Enriched Poset Polytopes. Ann. Comb. 28, 257–282 (2024). https://doi.org/10.1007/s00026-023-00679-7

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  • DOI: https://doi.org/10.1007/s00026-023-00679-7

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