### Abstract

In this paper we give Pfaffian or determinant expressions, and constant term identities for the conjectures in the paper "Self-complementary totally symmetric plane partitions" (J. Combin. Theory Ser. A 42, 277-292) by Mills, Robbins and Rumsey. We also settle a weak version of Conjecture 6 in the paper, i.e., the number of shifted plane partitions invariant under a certain involution is equal to the number of alternating sign matrices invariant under the vertical flip.

Original language | English |
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Publication status | Published - Dec 1 2007 |

Externally published | Yes |

Event | 19th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'07 - Tianjin, China Duration: Jul 2 2007 → Jul 6 2007 |

### Other

Other | 19th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'07 |
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Country | China |

City | Tianjin |

Period | 7/2/07 → 7/6/07 |

### Keywords

- Alternating sign matrices
- Constant term identities
- Determinants and Pfaffians
- Plane partitions
- Symmetric functions
- Symmetries

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Ishikawa, M. (2007).

*Refined enumerations of totally symmetric self-complementary plane partitions and constant term identities*. Paper presented at 19th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'07, Tianjin, China.