论文信息 - A direct bijection between descending plane partitions with no special parts and permutation matrices

A direct bijection between descending plane partitions with no special parts and permutation matrices

We present a direct bijection between descending plane partitions with no special parts and permutation matrices. This bijection has the desirable property that the number of parts of the descending plane partition corresponds to the inversion number of the permutation. Additionally, the number of maximum parts in the descending plane partition corresponds to the position of the one in the last column of the permutation matrix. We also discuss the possible extension of this approach to finding a bijection between descending plane partitions and alternating sign matrices.

Jessica Striker | Jessica Striker

[1] David P. Robbins,et al. Alternating Sign Matrices and Descending Plane Partitions , 1983, J. Comb. Theory, Ser. A.

[2] Arvind Ayyer,et al. A natural bijection between permutations and a family of descending plane partitions , 2009, Eur. J. Comb..

[3] P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[4] Paul Zinn-Justin,et al. On the weighted enumeration of alternating sign matrices and descending plane partitions , 2011, J. Comb. Theory, Ser. A.

[5] Jessica Striker,et al. A unifying poset perspective on alternating sign matrices, plane partitions, Catalan objects, tournaments, and tableaux , 2014, Adv. Appl. Math..

[6] D. Bressoud. Proofs and Confirmations: The Story of the Alternating-Sign Matrix Conjecture , 1999 .

[7] Andrea Sportiello,et al. Proof of the Razumov-Stroganov conjecture , 2010, J. Comb. Theory, Ser. A.

[8] Greg Kuperberg,et al. Another proof of the alternating sign matrix conjecture , 1996 .

[9] Pierre Lalonde. Alternating sign matrices with one -1 under vertical reflection , 2006, J. Comb. Theory, Ser. A.

[10] W. H. Mills,et al. Proof of the Macdonald conjecture , 1982 .

[11] Doron Zeilberger,et al. Proof of the alternating sign matrix conjecture , 1994, Electron. J. Comb..

[12] The poset perspective on alternating sign matrices , 2009, 0905.4495.