منابع مشابه
Puzzles, tableaux, and mosaics
We define mosaics, which are naturally in bijection with Knutson-Tao puzzles. We define an operation on mosaics, which shows they are also in bijection with Littlewood-Richardson skew-tableaux. Another consequence of this construction is that we obtain bijective proofs of commutativity and associativity for the ring structures defined either of these objects. In particular, we obtain a new, eas...
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This is an expository paper discussing some parallels between the Khovanov and knot Floer homologies. We describe the formal similarities between the theories, and give some examples which illustrate a somewhat mysterious correspondence between them.
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To record what has happened, ancient people tie knots. | I ching, the Chinese classic of 1027{771 B.C. Knots are fascinating objects. When fastening a rope, the distinction between a knot and a \slip-knot" (one that can be undone by pulling) must have been recognized very early in human history. We even developed a subconscious about knots: When we are puzzled or troubled, we have a feeling of ...
متن کاملQuantum knots and mosaics
In this paper, we give a precise and workable definition of a quantum knot system, the states of which are called quantum knots. This definition can be viewed as a blueprint for the construction of an actual physical quantum system. Moreover, this definition of a quantum knot system is intended to represent the “quantum embodiment” of a closed knotted physical piece of rope. A quantum knot, as ...
متن کاملGenetic mosaics.
Genetic mosaics can be used to gain insight into the cell specificity of gene function. How Caenorhabditis elegans mosaics are typically generated is reviewed, and several examples with relevance to developmental studies are mentioned. One example is mpk-1, which encodes a member of the Ras-MAP-kinase pathway. mpk-1 mosaics have been a means of studying the distinct cells that require the gene ...
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ژورنال
عنوان ژورنال: Journal of Knot Theory and Its Ramifications
سال: 2017
ISSN: 0218-2165,1793-6527
DOI: 10.1142/s0218216517500316