20 citations · 55 across the 18 of their papers we have counts for
18 papers
Combinatorics of semi-toric degenerations of Schubert varieties in type C
Naoki Fujita, Yuta Nishiyama
An approach to Schubert calculus is to realize Schubert classes as concrete combinatorial objects such as Schubert polynomials. Using the polytope ring of the Gelfand-Tsetlin polyt…
On combinatorics of string polytopes in types and
Yunhyung Cho, Naoki Fujita, Eunjeong Lee
A string polytope is a rational convex polytope whose lattice points parametrize a highest weight crystal basis, which is obtained from a string cone by explicit affine inequalitie…
Pairing optimization via statistics: Algebraic structure in pairing problems and its application to performance enhancement
Naoki Fujita, André Röhm, Takatomo Mihana +4
Fully pairing all elements of a set while attempting to maximize the total benefit is a combinatorically difficult problem. Such pairing problems naturally appear in various situat…
Efficient Pairing in Unknown Environments: Minimal Observations and TSP-based Optimization
Naoki Fujita, Nicolas Chauvet, Andre Roehm +4
Generating paired sequences with maximal compatibility from a given set is one of the most important challenges in various applications, including information and communication tec…
Semi-toric degenerations of Richardson varieties arising from cluster structures on flag varieties
Naoki Fujita
A toric degeneration of an irreducible variety is a flat degeneration to an irreducible toric variety. In the case of a flag variety, its toric degeneration with desirable properti…
Newton-Okounkov polytopes of flag varieties and marked chain-order polytopes
Naoki Fujita
Marked chain-order polytopes are convex polytopes constructed from a marked poset, which give a discrete family relating a marked order polytope with a marked chain polytope. In th…
Schubert calculus from polyhedral parametrizations of Demazure crystals
Naoki Fujita
One approach to Schubert calculus is to realize Schubert classes as concrete combinatorial objects such as Schubert polynomials. Through an identification of the cohomology ring of…
Fano and weak Fano Hessenberg varieties
Hiraku Abe, Naoki Fujita, Haozhi Zeng
Regular semisimple Hessenberg varieties are smooth subvarieties of the flag variety, and their examples contain the flag variety itself and the permutohedral variety which is a tor…
Newton-Okounkov bodies of flag varieties and combinatorial mutations
Naoki Fujita, Akihiro Higashitani
A Newton-Okounkov body is a convex body constructed from a projective variety with a globally generated line bundle and with a higher rank valuation on the function field, which gi…
Newton-Okounkov polytopes of Schubert varieties arising from cluster structures
Naoki Fujita, Hironori Oya
The theory of Newton-Okounkov bodies is a generalization of that of Newton polytopes for toric varieties, and it gives a systematic method of constructing toric degenerations of pr…
Polyhedral realizations of crystal bases and convex-geometric Demazure operators
Naoki Fujita
The main object in this paper is a certain rational convex polytope whose lattice points give a polyhedral realization of a highest weight crystal basis. This is also identical to…
Algebraic and geometric properties of flag Bott-Samelson varieties and applications to representations
Naoki Fujita, Eunjeong Lee, Dong Youp Suh
We introduce the notion of flag Bott-Samelson variety as a generalization of Bott-Samelson variety and flag variety. Using a birational morphism from an appropriate Bott-Samelson v…
Geometry of regular Hessenberg varieties
Hiraku Abe, Naoki Fujita, Haozhi Zeng
Let be a complex semisimple Lie algebra. For a regular element in and a Hessenberg space , we consider a regular Hessenbe…
Folding procedure for Newton-Okounkov polytopes of Schubert varieties
Naoki Fujita
The theory of Newton-Okounkov polytopes is a generalization of that of Newton polytopes for toric varieties, and it gives a systematic method of constructing toric degenerations of…
Khovanskii bases of Cox-Nagata rings and tropical geometry
Martha Bernal, Daniel Corey, Maria Donten-Bury +2
The Cox ring of a del Pezzo surface of degree 3 has a distinguished set of 27 minimal generators. We investigate conditions under which the initial forms of these generators genera…
A comparison of Newton-Okounkov polytopes of Schubert varieties
Naoki Fujita, Hironori Oya
A Newton-Okounkov body is a convex body constructed from a polarized variety with a valuation on its function field. Kaveh (resp., the first author and Naito) proved that the Newto…
Newton-Okounkov convex bodies of Schubert varieties and polyhedral realizations of crystal bases
Naoki Fujita, Satoshi Naito
A Newton-Okounkov convex body is a convex body constructed from a projective variety with a valuation on its homogeneous coordinate ring; this is deeply connected with representati…
Newton-Okounkov bodies for Bott-Samelson varieties and string polytopes for generalized Demazure modules
Naoki Fujita
A Newton-Okounkov convex body is a convex body constructed from a projective variety with a valuation on its homogeneous coordinate ring; this generalizes a Newton polytope for a t…