TY - JOUR

T1 - Identities in combinatorics III

T2 - Further aspects of ordered set sorting

AU - Andrews, George E.

AU - Bressoud, David M.

N1 - 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.

PY - 1984/5

Y1 - 1984/5

N2 - 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.

AB - 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.

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U2 - 10.1016/0012-365X(84)90159-6

DO - 10.1016/0012-365X(84)90159-6

M3 - Article

AN - SCOPUS:14744299553

SN - 0012-365X

VL - 49

SP - 223

EP - 236

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 3

ER -