Finite Posets and Ferrers Shapes

✍ Scribed by Thomas Britz; Sergey Fomin

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 627 KB
• Volume: 158
• Category: Article
• ISSN: 0001-8708
• DOI: 10.1006/aima.2000.1966

✦ Synopsis

(3.2) of the growth diagram for a permutation _. The following theorem shows that the shape * ij is uniquely determined by the shapes * i1, j&1 , * i, j&1 , and * i&1, j , together with knowing whether _(i)= j or not (i.e., whether (i, j) # P _ or not).

(2) If * i, j&1 =* i&1, j =* i&1, j&1 and _(i){ j, then * ij =* i&1, j&1 .

(3) If * i, j&1 =* i&1, j =* i&1, j&1 and _(i)= j, then * ij is obtained by adding a box to the first row of * i&1, j&1 .

(4) If * i, j&1 =* i&1, j {* i&1, j&1 , then * ij is obtained by adding a box to the row immediately below the box * i&1, j &* i&1, j&1 .