Some multivariate master polynomials for permutations, set partitions, and perfect matchings, and their continued fractions

We find Stieltjes-type and Jacobi-type continued fractions for some “master polynomials” that enumerate permutations, set partitions or perfect matchings with a large (sometimes infinite) number of simultaneous statistics. Our results contain many previously obtained identities as special cases, pro...

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Bibliographic Details
Published inAdvances in applied mathematics Vol. 138; p. 102341
Main Authors Sokal, Alan D., Zeng, Jiang
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.07.2022
Elsevier
Subjects
Continued fraction
Dyck path
Generating polynomial
J-fraction
Mathematics
Motzkin path
Perfect matching
Permutation
S-fraction
Set partition
secondary
Permutation
Set partition
Generating polynomial
S-fraction
Motzkin path
J-fraction
Dyck path
Perfect matching
primary
Continued fraction
Online AccessGet full text
ISSN0196-8858
1090-2074
DOI10.1016/j.aam.2022.102341

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Summary:We find Stieltjes-type and Jacobi-type continued fractions for some “master polynomials” that enumerate permutations, set partitions or perfect matchings with a large (sometimes infinite) number of simultaneous statistics. Our results contain many previously obtained identities as special cases, providing a common refinement of all of them.
ISSN:0196-8858
1090-2074
DOI:10.1016/j.aam.2022.102341