Zobrazeno 1 - 10
of 13
pro vyhledávání: '"Gaku Liu"'
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, Vol DMTCS Proceedings, 28th... (2020)
The dual stable Grothendieck polynomials are a deformation of the Schur functions, originating in the study of the K-theory of the Grassmannian. We generalize these polynomials by introducing a countable family of additional parameters such that the
Externí odkaz:
https://doaj.org/article/626815144f9641a581b7837a622ece4b
Autor:
Gaku Liu
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, Vol DMTCS Proceedings, 27th..., Iss Proceedings (2015)
In this extended abstract we consider mixed volumes of combinations of hypersimplices. These numbers, called mixed Eulerian numbers, were first considered by A. Postnikov and were shown to satisfy many properties related to Eulerian numbers, Catalan
Externí odkaz:
https://doaj.org/article/b21ac958b2bd4433bdba9338fba37117
Autor:
Gaku Liu
Publikováno v:
Discrete & Computational Geometry. 63:1-30
A flip is a minimal move between two triangulations of a polytope. The set of triangulations of a polytope was shown by Santos to not always be connected by flips, and it is an interesting problem to find large classes of polytopes for which it is. O
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5780add12ac5b5270188d734c0a5f117
https://doi.org/10.1007/s00454-019-00157-z
https://doi.org/10.1007/s00454-019-00157-z
Autor:
Gaku Liu
Publikováno v:
Discrete & Computational Geometry. 59:810-842
We give an example of a three-dimensional zonotope whose set of tight zonotopal tilings is not connected by flips. Using this, we show that the set of triangulations of $\Delta^4 \times \Delta^n$ is not connected by flips for large $n$. Our proof mak
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e2b44878c90f0f0bced569210a0d7fa9
https://doi.org/10.1007/s00454-018-9971-6
https://doi.org/10.1007/s00454-018-9971-6
Publikováno v:
Political Geography. 90:102414
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::3cf42aaf123bcd4214bb0fa992b84603
https://doi.org/10.1016/j.polgeo.2021.102414
https://doi.org/10.1016/j.polgeo.2021.102414
A cellular string of a polytope is a sequence of faces stacked on top of each other in a given direction. The poset of cellular strings, ordered by refinement, is known to be homotopy equivalent to a sphere. The subposet of coherent cellular strings
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c9b1a729eee85fbb77d96b39f593fd80
Autor:
Gaku Liu
Publikováno v:
Journal of Graph Theory. 78:28-42
Let $U_5$ be the tournament with vertices $v_1$, ..., $v_5$ such that $v_2 \rightarrow v_1$, and $v_i \rightarrow v_j$ if $j-i \equiv 1$, $2 \pmod{5}$ and ${i,j} \neq {1,2}$. In this paper we describe the tournaments which do not have $U_5$ as a subt
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::378152199a5d085935c89fc1404ec61b
https://doi.org/10.1002/jgt.21789
https://doi.org/10.1002/jgt.21789
Autor:
Gaku Liu, Stéphan Thomassé, Alex Scott, Felix Brandt, Ilhee Kim, Sergey Norin, Maria Chudnovsky, Paul Seymour
In 1990, motivated by applications in the social sciences, Thomas Schwartz made a conjecture about tournaments which would have had numerous attractive consequences. In particular, it implied that there is no tournament with a partition A, B of its v
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::57179331e84c28c7c60cbe0b356292e3
https://ora.ox.ac.uk/objects/uuid:a9ce3eeb-2997-4c35-b80e-406665318a52
https://ora.ox.ac.uk/objects/uuid:a9ce3eeb-2997-4c35-b80e-406665318a52
Autor:
Gaku Liu
The extension space conjecture of oriented matroid theory states that the space of all one-element, non-loop, non-coloop extensions of a realizable oriented matroid of rank $d$ has the homotopy type of a sphere of dimension $d-1$. We disprove this co
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bb5504fd56c6cf2a1954cd848407c754
http://arxiv.org/abs/1606.05033
http://arxiv.org/abs/1606.05033
The dual stable Grothendieck polynomials are a deformation of the Schur functions, originating in the study of the K-theory of the Grassmannian. We generalize these polynomials by introducing a countable family of additional parameters, and we prove
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e769e844fe9ce1acb630862f53ddd8ad
http://arxiv.org/abs/1509.03803
http://arxiv.org/abs/1509.03803