Polygraph Arrangements

✍ Scribed by Axel Hultman

• Book ID: 102570986
• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 235 KB
• Volume: 23
• Category: Article
• ISSN: 0195-6698
• DOI: 10.1006/eujc.2002.0613

✦ Synopsis

A class of subspace arrangements, Z (n, m), known as polygraph arrangements was exploited by Haiman in order to prove the n! theorem. By showing that their intersection lattices, L(Z (n, m)), are EL-shellable, we determine the cohomology groups of the complements of the arrangements. Moreover, we generalize the shellability results to a class of lattices which deserve to be called Dowling generalizations of L(Z (n, m)). As a consequence, we obtain the cohomology groups of the complements of certain Dowling analogues of polygraph arrangements.