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Quantum gravity and non-commutative spacetimes in three dimensions: a unified approach
, 2011 These notes summarise a talk surveying the combinatorial or Hamiltonian quantisation of three dimensional gravity in the Chern-Simons formulation, with an emphasis on the role of quantum groups and on the way the various physical constants (c,G,\Lambda ...
Schroers, Bernd J
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Transitive factorizations of permutations and geometry [PDF]
, 2014 We give an account of our work on transitive factorizations of permutations. The work has had impact upon other areas of mathematics such as the enumeration of graph embeddings, random matrices, branched covers, and the moduli spaces of curves.
Goulden, I. P., Jackson, D. M.
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Recent Conceptual Consequences of Loop Quantum Gravity. Part I: Foundational Aspects [PDF]
, 2001 Conceptual consequences of recent results in loop quantum gravity are collected and discussed here in view of their implications for a modern philosophy of science which is mainly understood as one that totalizes scientific insight so as to eventually ...
Zimmermann, Rainer E.
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Combinatorics of double loop suspensions, evaluation maps and Cohen groups
, 2019 We reformulate Milgram's model of a double loop suspension in terms of a preoperad of posets, each stage of which is the poset of all ordered partitions of a finite set. Using this model, we give a combinatorial model for the evaluation map and use it to
Huang, Ruizhi, Wu, Jie
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ALCOVE PATHS AND GELFAND-TSETLIN PATTERNS (Representation Theory and its Combinatorial Aspects)
, 2020 英也 渡邉
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Half-integrality of the $KGB$ decomposition for SL$_3$ (Representation Theory and its Combinatorial Aspects)本稿では[5]に基づき, 軌道分解の組合せ論に関する一般的なアイデアと, その例であるZ[1/2]上のSL3の旗概形のS0(3)不変部分空間への分解について概説する.
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Several classes of plane partitions with the same generating function (Representation Theory and its Combinatorial Aspects)StrikerとWilliamsはrc-posetという概念を定義してpromotionやrowmotionをtoggleという概念を使ってrc-posetの順序イデアル全体になす分配束に一般化できることを示した. また, 交代符号行列全体の成す分配束に対して, join-irreducibleな元全体の成す部分半順序集合AnがA型のpositive root posetsΦ(Ak)を貼り合わせてできることを示した. この原稿の中で我々は点対称な交代符号行列の成す有限分配束について調べる.
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