Identities in combinatorics III: Further aspects of ordered set sorting

George E. Andrews; David M. Bressoud

doi:10.1016/0012-365X(84)90159-6

Identities in combinatorics III: Further aspects of ordered set sorting

George E. Andrews
, David M. Bressoud

Mathematics

Research output: Contribution to journal › Article › peer-review

24 Scopus citations

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.

Original language	English (US)
Pages (from-to)	223-236
Number of pages	14
Journal	Discrete Mathematics
Volume	49
Issue number	3
DOIs	https://doi.org/10.1016/0012-365X(84)90159-6
State	Published - May 1984

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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

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@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<\textasciitilde{}a2\textasciitilde{} .. .<-an\}, and qJ: \{bl \textasciitilde{}< b2 \textasciitilde{}<{"} • • \textasciitilde{}< bin\}. The crossing number of \textasciitilde{}b with respect to 1r starting at n is defined as the largest r for which b,<a\textasciitilde{}\_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 \textbackslash{}[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",

}

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.

UR - https://www.scopus.com/pages/publications/14744299553

UR - https://www.scopus.com/pages/publications/14744299553#tab=citedBy

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 -

Identities in combinatorics III: Further aspects of ordered set sorting

Abstract

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