19-23 June 2023
Faculty of Physics, University of Warsaw
Europe/Warsaw timezone
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A natural signed bijection between monotone triangles and shifted Gelfand-Tsetlin patterns

Presented by Mr. Takuya INOUE

Content

The alternating sign matrices-descending plane partitions (ASM-DPP) bijection problem is one of the most intriguing open problems in integrable combinatorics. Recently, Fischer and Konvalinka have obtained a bijection between ASM(n) × DPP(n−1) and DPP(n) × ASM(n−1) using the notions of a signed set and a signed bijection and which involves an explicit construction of a signed bijection between alternating sign matrices and so-called shifted Gelfand-Tsetlin patterns. Their proof can be considered as a combinatorial proof of the enumeration of ASM. We define the notion of compatibility of a signed bijection to measure its naturalness and we use it to simplify said signed bijection between alternating sign matrices and shifted Gelfand-Tsetlin patterns, thereby providing a better combinatorial proof of the enumeration of ASM.

Place

Location: Faculty of Physics, University of Warsaw
Address: Pasteura 5, Warsaw
Room: Lecture hall: 0.06

Primary authors

  • Mr. Takuya INOUE Graduate School of Mathematical Sciences, The University of Tokyo
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