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Plateau-Descent Joint Symmetry on Qu...

Drennan, Michael,

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Plateau-Descent Joint Symmetry on Quasi-Stirling Permutations /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Plateau-Descent Joint Symmetry on Quasi-Stirling Permutations // Michael Drennan.
作者:	Drennan, Michael,
面頁冊數:	1 electronic resource (151 pages)
附註:	Source: Dissertations Abstracts International, Volume: 87-01, Section: B.
Contained By:	Dissertations Abstracts International87-01B.
標題:	Mathematics. -
電子資源:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=32117035
ISBN:	9798288805394

Plateau-Descent Joint Symmetry on Quasi-Stirling Permutations /
Drennan, Michael,

Plateau-Descent Joint Symmetry on Quasi-Stirling Permutations /Michael Drennan. - 1 electronic resource (151 pages)

Source: Dissertations Abstracts International, Volume: 87-01, Section: B.

Stirling permutations, STn, are permutations of the multiset [0,0,1,1,...,n,n] which avoid the pattern 212. Elizalde showed, extending a result from Bona, that the bivariate generating function for the plateau and descent statistics, P and D, respectively, is jointly symmetric over STn. This dissertation considers an extension of the Stirling permutations introduced by Archer et al. called the Quasi-Stirling permutations, Qn. Quasi-Stirling permutations generalize Stirling permutations by requiring only that patterns 1212 and 2121 are avoided. While the P and D statistics extend naturally onto Qn the corresponding bivariate generating function is no longer symmetric. We propose a new statistic, Pd, which reduces to P over the Stirling permutations, and we conjecture produces a jointly symmetric generating function with D over Qn. We prove this symmetry for a subset of Qn in two ways using both a finer partition of the descent statistic as well as a recursion on intransitive trees. This work features heavily the combinatorial analysis of rooted edge labeled plane trees, rooted vertex labeled binary plane trees and intransitive bipartite trees. We generalize the connection to bipartite trees by introducing a new notation which generates tripartite graphs and conjecture the existence of a map on these objects which demonstrates the Pd-D joint symmetry on all of Qn.

English

ISBN: 9798288805394Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Stirling permutations

Plateau-Descent Joint Symmetry on Quasi-Stirling Permutations /
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520 $a Stirling permutations, STn, are permutations of the multiset [0,0,1,1,...,n,n] which avoid the pattern 212. Elizalde showed, extending a result from Bona, that the bivariate generating function for the plateau and descent statistics, P and D, respectively, is jointly symmetric over STn. This dissertation considers an extension of the Stirling permutations introduced by Archer et al. called the Quasi-Stirling permutations, Qn. Quasi-Stirling permutations generalize Stirling permutations by requiring only that patterns 1212 and 2121 are avoided. While the P and D statistics extend naturally onto Qn the corresponding bivariate generating function is no longer symmetric. We propose a new statistic, Pd, which reduces to P over the Stirling permutations, and we conjecture produces a jointly symmetric generating function with D over Qn. We prove this symmetry for a subset of Qn in two ways using both a finer partition of the descent statistic as well as a recursion on intransitive trees. This work features heavily the combinatorial analysis of rooted edge labeled plane trees, rooted vertex labeled binary plane trees and intransitive bipartite trees. We generalize the connection to bipartite trees by introducing a new notation which generates tripartite graphs and conjecture the existence of a map on these objects which demonstrates the Pd-D joint symmetry on all of Qn.
546 $a English
590 $a School code: 0243
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
653 $a Stirling permutations
653 $a Joint symmetry
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690 $a 0642
710 2 $a The University of Vermont and State Agricultural College. $b Mathematical Sciences. $e degree granting institution. $3 3823222
720 1 $a Lee, Byung $e degree supervisor.
720 1 $a Warrington, Gregory $e degree supervisor.
773 0 $t Dissertations Abstracts International $g 87-01B.
790 $a 0243
791 $a Ph.D.
792 $a 2025
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=32117035