### 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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Title of host publication | FPSAC'07 - 19th International Conference on Formal Power Series and Algebraic Combinatorics |

Publication status | Published - 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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*FPSAC'07 - 19th International Conference on Formal Power Series and Algebraic Combinatorics*

**Refined enumerations of totally symmetric self-complementary plane partitions and constant term identities.** / Ishikawa, Masao.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*FPSAC'07 - 19th International Conference on Formal Power Series and Algebraic Combinatorics.*19th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'07, Tianjin, China, 7/2/07.

}

TY - GEN

T1 - Refined enumerations of totally symmetric self-complementary plane partitions and constant term identities

AU - Ishikawa, Masao

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

KW - Alternating sign matrices

KW - Constant term identities

KW - Determinants and Pfaffians

KW - Plane partitions

KW - Symmetric functions

KW - Symmetries

UR - http://www.scopus.com/inward/record.url?scp=84860720163&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84860720163&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84860720163

BT - FPSAC'07 - 19th International Conference on Formal Power Series and Algebraic Combinatorics

ER -