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Enumeration of Non-Intersecting Path...

Lee, Yi-Lin,

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Enumeration of Non-Intersecting Paths and Related Tiling Problems /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Enumeration of Non-Intersecting Paths and Related Tiling Problems // Yi-Lin Lee.
作者:	Lee, Yi-Lin,
面頁冊數:	1 electronic resource (116 pages)
附註:	Source: Dissertations Abstracts International, Volume: 86-11, Section: B.
Contained By:	Dissertations Abstracts International86-11B.
標題:	Theoretical mathematics. -
電子資源:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31993797
ISBN:	9798314885130

Enumeration of Non-Intersecting Paths and Related Tiling Problems /
Lee, Yi-Lin,

Enumeration of Non-Intersecting Paths and Related Tiling Problems /Yi-Lin Lee. - 1 electronic resource (116 pages)

Source: Dissertations Abstracts International, Volume: 86-11, Section: B.

We provide new techniques to enumerate non-intersecting lattice paths. Our work extends the Lindstrom-Gessel-Viennot theorem, which provides the "straight" enumeration of weighted non-intersecting lattice paths, expressing it as a determinant whose entries are signed counts of lattice paths with given starting and ending points. This extension can be applied to enumerate tilings of a region with arbitrary holes. We also introduce a new symmetry class of domino tilings of the Aztec diamond, called the off-diagonal symmetry class. With a modification of Stembridge's Pfaffian formula, we prove several results for this new symmetry class, including: (1) the number of off-diagonally symmetric domino tilings of the Aztec diamond is given by a Pfaffian, where the entries of the matrix satisfy a simple recurrence relation, (2) the symmetry property for the off-diagonal symmetry class in which the Aztec diamond has one boundary defect, and (3) the relation between the "nearly" off-diagonal symmetry class and the off-diagonal symmetry class with one boundary defect.

English

ISBN: 9798314885130Subjects--Topical Terms:

3173530
Theoretical mathematics.
Subjects--Index Terms:

Aztec diamond

Enumeration of Non-Intersecting Paths and Related Tiling Problems /
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300 $a 1 electronic resource (116 pages)
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500 $a Source: Dissertations Abstracts International, Volume: 86-11, Section: B.
500 $a Advisors: Ciucu, Mihai Committee members: Larsen, Michael; Strauch, Matthias; Thurston, Dylan.
502 $b Ph.D. $c Indiana University $d 2025.
520 $a We provide new techniques to enumerate non-intersecting lattice paths. Our work extends the Lindstrom-Gessel-Viennot theorem, which provides the "straight" enumeration of weighted non-intersecting lattice paths, expressing it as a determinant whose entries are signed counts of lattice paths with given starting and ending points. This extension can be applied to enumerate tilings of a region with arbitrary holes. We also introduce a new symmetry class of domino tilings of the Aztec diamond, called the off-diagonal symmetry class. With a modification of Stembridge's Pfaffian formula, we prove several results for this new symmetry class, including: (1) the number of off-diagonally symmetric domino tilings of the Aztec diamond is given by a Pfaffian, where the entries of the matrix satisfy a simple recurrence relation, (2) the symmetry property for the off-diagonal symmetry class in which the Aztec diamond has one boundary defect, and (3) the relation between the "nearly" off-diagonal symmetry class and the off-diagonal symmetry class with one boundary defect.
546 $a English
590 $a School code: 0093
650 4 $a Theoretical mathematics. $3 3173530
650 4 $a Mathematics. $3 515831
650 4 $a Applied mathematics. $3 2122814
653 $a Aztec diamond
653 $a Lattice paths
653 $a Domino tilings
653 $a Symmetry classes
653 $a Boundary defect
690 $a 0642
690 $a 0405
690 $a 0364
710 2 $a Indiana University. $b Mathematics. $e degree granting institution. $3 3823079
720 1 $a Ciucu, Mihai $e degree supervisor.
773 0 $t Dissertations Abstracts International $g 86-11B.
790 $a 0093
791 $a Ph.D.
792 $a 2025
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31993797