Chains of Length 2 in Fillings of Layer Polyominoes Academic Article

abstract

• The symmetry of the joint distribution of the numbers of crossings and nestings of length 2 has been observed in many combinatorial structures, including permutations, matchings, set partitions, linked partitions, and certain families of graphs. These results have been unified in the larger context of enumeration of northeast and southeast chains of length 2 in 01-fillings of moon polyominoes. In this paper we extend this symmetry to fillings of a more general family-layer polyominoes, which are intersection-free and row-convex, but not necessarily column-convex. Our main result is that the joint distribution of the numbers of northeast and southeast chains of length 2 over 01-fillings is symmetric and invariant under an arbitrary permutation of rows.

authors

• Yan, Catherine

published proceedings

• ELECTRONIC JOURNAL OF COMBINATORICS

author list (cited authors)

• Phillipson, M., Yan, C. H., & Yeh, J.

complete list of authors

• Phillipson, Mitch||Yan, Catherine H||Yeh, Jean

publication date

• September 2013

publisher

• The Electronic Journal of Combinatorics  Publisher

published in

• The Electronic Journal of Combinatorics  Journal

keywords

• Chains Of Length 2
• Polyomino
• Symmetric Distributions

URI

• https://hdl.handle.net/1969.1/180711

volume

• 20

issue

• 3