1 / 13

1 0 0 –1 1 0 –1 0 1

1979, Andrews counts cyclically symmetric plane partitions. 1 0 0 –1 1 0 –1 0 1. 1979, Andrews counts cyclically symmetric plane partitions. 1 0 0 –1 1 0 –1 0 1. 1979, Andrews counts cyclically symmetric plane partitions. 1 0 0 –1 1 0 –1 0 1.

vlorenzo
Télécharger la présentation

1 0 0 –1 1 0 –1 0 1

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 1979, Andrews counts cyclically symmetric plane partitions 1 0 0 –1 1 0 –1 0 1

  2. 1979, Andrews counts cyclically symmetric plane partitions 1 0 0 –1 1 0 –1 0 1

  3. 1979, Andrews counts cyclically symmetric plane partitions 1 0 0 –1 1 0 –1 0 1

  4. 1979, Andrews counts cyclically symmetric plane partitions 1 0 0 –1 1 0 –1 0 1

  5. 1979, Andrews counts cyclically symmetric plane partitions 1 0 0 –1 1 0 –1 0 1 L1 = W1 > L2 = W2 > L3 = W3 > … width length

  6. 1979, Andrews counts descending plane partitions 1 0 0 –1 1 0 –1 0 1 L1 > W1 ≥ L2 > W2 ≥ L3 > W3 ≥ … 6 6 6 4 3 3 3 2 width length

  7. 6 X 6 ASM  DPP with largest part ≤ 6 What are the corresponding 6 subsets of DPP’s? 1 0 0 –1 1 0 –1 0 1 6 6 6 4 3 3 3 2 width length

  8. ASM with 1 at top of first column DPP with no parts of size n. ASM with 1 at top of last column DPP with n–1 parts of size n. 1 0 0 –1 1 0 –1 0 1 6 6 6 4 3 3 3 2 width length

  9. Mills, Robbins, Rumsey Conjecture: # of n by n ASM’s with 1 at top of column j equals # of DPP’s ≤ n with exactly j–1 parts of size n. 1 0 0 –1 1 0 –1 0 1 6 6 6 4 3 3 3 2 width length

  10. Mills, Robbins, & Rumsey proved that # of DPP’s ≤ n with j parts of size n was given by their conjectured formula for ASM’s. 1 0 0 –1 1 0 –1 0 1

  11. Mills, Robbins, & Rumsey proved that # of DPP’s ≤ n with j parts of size n was given by their conjectured formula for ASM’s. 1 0 0 –1 1 0 –1 0 1 Discovered an easier proof of Andrews’ formula, using induction on j and n.

  12. Mills, Robbins, & Rumsey proved that # of DPP’s ≤ n with j parts of size n was given by their conjectured formula for ASM’s. 1 0 0 –1 1 0 –1 0 1 Discovered an easier proof of Andrews’ formula, using induction on j and n. Used this inductive argument to prove Macdonald’s conjecture “Proof of the Macdonald Conjecture,” Inv. Math., 1982

  13. Mills, Robbins, & Rumsey proved that # of DPP’s ≤ n with j parts of size n was given by their conjectured formula for ASM’s. 1 0 0 –1 1 0 –1 0 1 Discovered an easier proof of Andrews’ formula, using induction on j and n. Used this inductive argument to prove Macdonald’s conjecture “Proof of the Macdonald Conjecture,” Inv. Math., 1982 But they still didn’t have a proof of their conjecture!

More Related