Adler V.E. On the combinatorics of several integrable hierarchies, talk at The Mini-Workshop on Integrable Equations, 17 February 2015, Independent University of Moscow (abstract): Difference between revisions
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| title = On the combinatorics of several integrable hierarchies | | title = On the combinatorics of several integrable hierarchies | ||
| abstract = We establish a correspondence between the generating functions related to some integrable hierarchies and certain classes of set partitions. In a sense, the inverse problem of enumerative combinatorics is considered: given a prescribed statistics, to figure out a definition of the corresponding combinatorial objects. The answer for the potential Burgers hierarchy is rather well known: set partitions, Bell polynomials, Stirling numbers of the 2nd kind, Bell numbers. An analogous correspondence for the KdV hierarchy (non-overlapping partitions, Bessel numbers) and Ibragimov–Shabat hierarchy (B type partitions, Dowling numbers) is new. | | abstract = We establish a correspondence between the generating functions related to some integrable hierarchies and certain classes of set partitions. In a sense, the inverse problem of enumerative combinatorics is considered: given a prescribed statistics, to figure out a definition of the corresponding combinatorial objects. The answer for the potential Burgers hierarchy is rather well known: set partitions, Bell polynomials, Stirling numbers of the 2nd kind, Bell numbers. An analogous correspondence for the KdV hierarchy (non-overlapping partitions, Bessel numbers) and Ibragimov–Shabat hierarchy (B type partitions, Dowling numbers) is new. | ||
| slides = [http://matphys.itp.ac.ru/talks/Coefficients_talk_MCCME_2015_02_17.pdf http://matphys.itp.ac.ru/talks/Coefficients_talk_MCCME_2015_02_17.pdf], [[Media:Coefficients_talk_MCCME_2015_02_17.pdf|local copy]] | | slides = [http://matphys.itp.ac.ru/talks/Coefficients_talk_MCCME_2015_02_17.pdf http://matphys.itp.ac.ru/talks/Coefficients_talk_MCCME_2015_02_17.pdf], [[Media:Coefficients_talk_MCCME_2015_02_17.pdf|local copy]] | ||
[http://matphys.itp.ac.ru/talks/Coefficients_talk_ITP_2015_01_16.pdf http://matphys.itp.ac.ru/talks/Coefficients_talk_ITP_2015_01_16.pdf], [[Media:Coefficients_talk_ITP_2015_01_16.pdf|local copy]] (in Russian) | |||
| references = Adler V.E. On the combinatorics of several integrable hierarchies, {{arXiv|1501.06086}} | | references = Adler V.E. On the combinatorics of several integrable hierarchies, {{arXiv|1501.06086}} | ||
| 79YY-MM-DD = 7984-97-84 | | 79YY-MM-DD = 7984-97-84 | ||
}} | }} | ||
Latest revision as of 08:46, 19 February 2015
Speaker: Vsevolod Adler
Title: On the combinatorics of several integrable hierarchies
Abstract:
We establish a correspondence between the generating functions related to some integrable hierarchies and certain classes of set partitions. In a sense, the inverse problem of enumerative combinatorics is considered: given a prescribed statistics, to figure out a definition of the corresponding combinatorial objects. The answer for the potential Burgers hierarchy is rather well known: set partitions, Bell polynomials, Stirling numbers of the 2nd kind, Bell numbers. An analogous correspondence for the KdV hierarchy (non-overlapping partitions, Bessel numbers) and Ibragimov–Shabat hierarchy (B type partitions, Dowling numbers) is new.
Slides: http://matphys.itp.ac.ru/talks/Coefficients_talk_MCCME_2015_02_17.pdf, local copy
http://matphys.itp.ac.ru/talks/Coefficients_talk_ITP_2015_01_16.pdf, local copy (in Russian)
References:
Adler V.E. On the combinatorics of several integrable hierarchies, arXiv:1501.06086