q-Narayana numbers and the flag h-vector
2004 (English)In: Discrete Mathematics, ISSN 0012-365X, E-ISSN 1872-681X, Vol. 281, no 03-jan, 67-81 p.Article in journal (Refereed) Published
The Narayana numbers are N(n,k) = (1/n)((n)(k))((n)(k+1)). There are several natural statistics on Dyck paths with a distribution given by N(n, k). We show the equidistribution of Narayana statistics by computing the flag h-vector of J(2 x n) in different ways. In the process we discover new Narayana statistics and provide co-statistics for the Narayana statistics so that the bi-statistics have a distribution given by Furlinger and Hofbauer's q-Narayana numbers. We interpret the flag h-vector in terms of semi-standard Young tableaux, which enables us to express the q-Narayana numbers in terms of Schur functions. We also introduce what we call pre-shellings of simplicial complexes.
Place, publisher, year, edition, pages
2004. Vol. 281, no 03-jan, 67-81 p.
Narayana numbers, flag h-vector, Schur function, shelling, catalan path statistics, enumerative property, combinatorial, partitions
IdentifiersURN: urn:nbn:se:kth:diva-23318ISI: 000220752100005OAI: oai:DiVA.org:kth-23318DiVA: diva2:342016
QC 201005252010-08-102010-08-10Bibliographically approved