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Guillotine cuts & pattern avoidance in permutations

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dc.contributor.author Jain, Siddhartha
dc.contributor.author Raman, Rajiv (Advisor)
dc.contributor.author Ram, Samrith (Advisor)
dc.date.accessioned 2019-10-09T09:47:54Z
dc.date.available 2019-10-09T09:47:54Z
dc.date.issued 2019-04-15
dc.identifier.uri http://repository.iiitd.edu.in/xmlui/handle/123456789/785
dc.description.abstract Given a set of axis-parallel rectangles on a plane, can you cut out a constant fraction of them using only Guillotine cuts? We try to answer this question in the project. The general problem of cutting out convex sets was investigated by Pach & Tardos [11]. But there has been a lot of interest in proving better bounds for rectangles. This is because if the answer to the aforementioned question is in the affirmative, it automatically gives us a polytime O(1)-approximation to MISR, as stressed in a paper by Abed, Chalermsook et al. [1], which made progress by showing abound of n=81 for the special case of squares. In our investigation of these structures, a strong connection with permutations showed up. This was mainly due to a combinatorial bijection between Floorplans and Baxter permutations given by Ackerman et al. [2]. Combined with the work of Young et al. [13], it inspired a strategy to prove bounds which work for all rectangle sets: delete just enough rectangles to delete all pinwheels, which we de ne. Moreover, previously unexplored (seemingly) yet natural questions about the eld of Pattern Matching / Avoidance in Permutations presented themselves in our study. We detail numerous results and conjectures in this area. en_US
dc.language.iso en_US en_US
dc.publisher IIITD-Delhi en_US
dc.subject Combinatorial Geometry en_US
dc.subject Geometry en_US
dc.subject Rectangles en_US
dc.subject Permutations en_US
dc.subject Pattern Matching en_US
dc.subject Guillotine cuts en_US
dc.subject Independent Sets en_US
dc.title Guillotine cuts & pattern avoidance in permutations en_US
dc.type Other en_US

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