Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8903685 | Journal of Combinatorial Theory, Series A | 2019 | 28 Pages |
Abstract
If we have 1,2âR and if for all nâR with n odd and nâ¥3, we have n±1âR, we additionally show that each entry of [{nk}R]n,kâ¥1â1, [[nk]R]â1n,kâ¥1 and [L(n,k)R]n,kâ¥1â1 is up to an explicit sign the cardinality of a single explicitly defined family of labeled forests. With R as before we also do the same for restriction sets of the form R(d)={d(râ1)+1:râR} for all dâ¥1. Our results also provide combinatorial interpretations of the kth Whitney numbers of the first and second kinds of Î n1,d, the poset of partitions of [n] that have each part size congruent to 1 mod d.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
John Engbers, David Galvin, Cliff Smyth,