@article{d21d844b038a422f815c4cf2394d8de0,
title = "Identities in combinatorics III: Further aspects of ordered set sorting",
abstract = "Given two multi-sets of non-negative integers, we define a measure of their common values called the crossing number and then use this concept to provide a combinatorial interpretation of the q-Hahn polynomials and combinatorial proofs of the q-analogs of the Pfaff-Saalschutz summation and the Sheppard transformation.",
author = "Andrews, {George E.} and Bressoud, {David M.}",
note = "Funding Information: The simplest example of the crossing number is in connection with two nondecreasing finite sequences of positive integers 1r:{al<~a2~ .. .<-an}, and qJ: {bl ~< b2 ~<{"} • • ~< bin}. The crossing number of ~b with respect to 1r starting at n is defined as the largest r for which b,<a~_r+l. If the a's and b's are positive then the crossing number is most easily understood by viewing the a's and b's as partitions and looking at their Ferrers graphs \[2; p. 6if.I, the a's in English notation (largest part on top), the b's in French (smallest part on top). For * Partially supported by N.S.F. grants. ** Partially supported by N.S.F. grants and a fellowship from the Sloan Foundation.",
year = "1984",
month = may,
doi = "10.1016/0012-365X(84)90159-6",
language = "English (US)",
volume = "49",
pages = "223--236",
journal = "Discrete Mathematics",
issn = "0012-365X",
publisher = "Elsevier B.V.",
number = "3",
}