Zobrazeno 1 - 10
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pro vyhledávání: '"Nakanishi A"'
Autor:
Nakanishi, Misa
Lov\'{a}sz conjectured that every connected vertex-transitive graph contains a hamilton path in 1970. First we reveal the structure of connected vertex-transitive graphs with an odd number of vertices. Then we prove that every connected vertex-transi
Externí odkaz:
http://arxiv.org/abs/2407.00646
Autor:
Nakanishi, Tomoki
We formulate the pentagon relation for quantum dilogarithm elements in the structure group of a quantum cluster scattering diagram (QCSD). As an application, we show the nonpositivity of a certain class of nonskew-symmetric QCSDs. Also, we explicitly
Externí odkaz:
http://arxiv.org/abs/2202.01588
Autor:
Nakanishi, Tomoki
Publikováno v:
MSJ Mem. 41 (2023)
This is a first step guide to the theory of cluster algebras. We especially focus on basic notions, techniques, and results concerning seeds, cluster patterns, and cluster algebras.
Comment: v1: 80 pp; v2: 82 pp, Prop 2.4 corrected, index added;
Comment: v1: 80 pp; v2: 82 pp, Prop 2.4 corrected, index added;
Externí odkaz:
http://arxiv.org/abs/2201.11371
Publikováno v:
Int. Math. Res. Not. 2024 (2024) 613-634
We discuss a product formula for $F$-polynomials in cluster algebras, and provide two proofs. One proof is inductive and uses only the mutation rule for $F$-polynomials. The other is based on the Fock-Goncharov decomposition of mutations. We conclude
Externí odkaz:
http://arxiv.org/abs/2112.11839
Autor:
Nakanishi, Tomoki
Publikováno v:
Nagoya Math. J. 253 (2024) 1-22
We extend the notion of $y$-variables (coefficients) in cluster algebras to cluster scattering diagrams. Accordingly, we extend the dilogarithm identity associated with a period in a cluster pattern to the one associated with a loop in a cluster scat
Externí odkaz:
http://arxiv.org/abs/2111.09555
Autor:
Nakanishi, Tomoki
Publikováno v:
MSJ Mem. 41 (2023)
This is a self-contained exposition of several fundamental properties of cluster scattering diagrams introduced and studied by Gross, Hacking, Keel, and Kontsevich. In particular, detailed proofs are presented for the construction, the mutation invar
Externí odkaz:
http://arxiv.org/abs/2111.00800
Autor:
Nakanishi, Tomoki
Publikováno v:
MSJ Mem. 41 (2023)
We review some important results by Gross, Hacking, Keel, and Kontsevich on cluster algebra theory, namely, the column sign-coherence of $C$-matrices and the Laurent positivity, both of which were conjectured by Fomin and Zelevinsky. We digest and re
Externí odkaz:
http://arxiv.org/abs/2103.16309
Autor:
Gekhtman, Michael, Nakanishi, Tomoki
Publikováno v:
Experimental Mathematics 31 (2022) 497-505
The sign coherence phenomenon is an important feature of c-vectors in cluster algebras with principal coefficients. In this note, we consider a more general version of c-vectors defined for arbitrary cluster algebras of geometric type and formulate a
Externí odkaz:
http://arxiv.org/abs/1904.00971
Autor:
Nakanishi, Misa
In this paper, we consider generalized domination structure in graphs, which stipulates the structure of a minimum dominating set. Two cycles of length 0 mod 3 intersecting with one path are the constituents of the domination structure and by taking
Externí odkaz:
http://arxiv.org/abs/1901.10781
Autor:
Nakanishi, Misa
From the research of several recent papers, we are concerned with domination number in cubic graphs and give a sufficient condition for Reed's conjecture.
Comment: text overlap with arXiv:1711.07587
Comment: text overlap with arXiv:1711.07587
Externí odkaz:
http://arxiv.org/abs/1809.08987