2026-09-19T03:25:07Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/734442022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Alexander Postnikov.
Lewis, Joel Brewster
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2012-09-27T18:23:35Z
2012-09-27T18:23:35Z
2012
2012
http://hdl.handle.net/1721.1/73444
809654848
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Cataloged from student submitted PDF version of thesis.
Includes bibliographical references (p. 67-69).
We consider a variety of questions related to pattern avoidance in alternating permutations and generalizations thereof. We give bijective enumerations of alternating permutations avoiding patterns of length 3 and 4, of permutations that are the reading words of a "thickened staircase" shape (or equivalently of permutations with descent set {k, 2k, 3k, . . .}) avoiding a monotone pattern, and of the reading words of Young tableaux of any skew shape avoiding any of the patterns 132, 213, 312, or 231. Our bijections include a simple bijection involving binary trees, variations on the Robinson-Schensted-Knuth correspondence, and recursive bijections established via isomorphisms of generating trees.
by Joel Brewster Lewis.
Ph.D.
69 p.
eng
Massachusetts Institute of Technology
M.I.T. theses are protected by
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http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
Pattern avoidance for alternating permutations and reading words of tableaux
Thesis
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<Abstract>We consider a variety of questions related to pattern avoidance in alternating permutations and generalizations thereof. We give bijective enumerations of alternating permutations avoiding patterns of length 3 and 4, of permutations that are the reading words of a "thickened staircase" shape (or equivalently of permutations with descent set {k, 2k, 3k, . . .}) avoiding a monotone pattern, and of the reading words of Young tableaux of any skew shape avoiding any of the patterns 132, 213, 312, or 231. Our bijections include a simple bijection involving binary trees, variations on the Robinson-Schensted-Knuth correspondence, and recursive bijections established via isomorphisms of generating trees.</Abstract>
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