## Antichains of interval orders and semiorders, and Dilworth lattices of maximum size antichains

##### Author(s)

Engel Shaposhnik, Efrat
DownloadFull printable version (4.517Mb)

##### Other Contributors

Massachusetts Institute of Technology. Department of Mathematics.

##### Advisor

Richard P. Stanley.

##### Terms of use

##### Metadata

Show full item record##### Abstract

This thesis consists of two parts. In the first part we count antichains of interval orders and in particular semiorders. We associate a Dyck path to each interval order, and give a formula for the number of antichains of an interval order in terms of the corresponding Dyck path. We then use this formula to give a generating function for the total number of antichains of semiorders, enumerated by the sizes of the semiorders and the antichains. In the second part we expand the work of Liu and Stanley on Dilworth lattices. Let L be a distributive lattice, let -(L) be the maximum number of elements covered by a single element in L, and let K(L) be the subposet of L consisting of the elements that cover o-(L) elements. By a result of Dilworth, K(L) is also a distributive lattice. We compute o(L) and K(L) for various lattices L that arise as the coordinate-wise partial ordering on certain sets of semistandard Young tableaux.

##### Description

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016. Cataloged from PDF version of thesis. Includes bibliographical references (page 87).

##### Date issued

2016##### Department

Massachusetts Institute of Technology. Department of Mathematics.##### Publisher

Massachusetts Institute of Technology

##### Keywords

Mathematics.