Zobrazeno 1 - 10
of 54
pro vyhledávání: '"Pavlo Pylyavskyy"'
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, Vol DMTCS Proceedings, 28th... (2020)
In his study of Kazhdan-Lusztig cells in affine type A, Shi has introduced an affine analog of Robinson- Schensted correspondence. We generalize the Matrix-Ball Construction of Viennot and Fulton to give a more combi- natorial realization of Shi's al
Externí odkaz:
https://doaj.org/article/c04ae9caf380465c88e4025404737211
Autor:
Rebecca Patrias, Pavlo Pylyavskyy
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, Vol DMTCS Proceedings, 27th..., Iss Proceedings (2015)
We define a $K$ -theoretic analogue of Fomin’s dual graded graphs, which we call dual filtered graphs. The key formula in the definition is $DU - UD = D + I$. Our major examples are $K$ -theoretic analogues of Young’s lattice, the binary tree, an
Externí odkaz:
https://doaj.org/article/7a4790bf746745f4afea96f934d60d69
Autor:
Max Glick, Pavlo Pylyavskyy
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, Vol DMTCS Proceedings, 27th..., Iss Proceedings (2015)
We introduce a rich family of generalizations of the pentagram map sharing the property that each generates an infinite configuration of points and lines with four points on each line. These systems all have a description as $Y$ -mutations in a clust
Externí odkaz:
https://doaj.org/article/f2e47655cc2d42e5be30b2b4b8a2a049
Autor:
Dongkwan Kim, Pavlo Pylyavskyy
Publikováno v:
Algebraic Combinatorics. 6:213-241
Autor:
Dongkwan Kim, Pavlo Pylyavskyy
Publikováno v:
International Mathematics Research Notices.
The affine matrix-ball construction (abbreviated AMBC) was developed by Chmutov, Lewis, Pylyavskyy, and Yudovina as an affine generalization of the Robinson–Schensted correspondence. We show that AMBC gives a simple way to compute a distinguished i
Publikováno v:
Journal of Combinatorial Algebra. 4:111-140
Berenstein and Kirillov have studied the action of Bender-Knuth moves on semistandard tableaux. Losev has studied a cactus group action in Kazhdan-Lusztig theory; in type $A$ this action can also be identified in the work of Henriques and Kamnitzer.
Publikováno v:
Annales de l’Institut Henri Poincaré D. 7:249-302
We consider a family of cellular automata $\Phi(n,k)$ associated with infinite reduced elements on the affine symmetric group $\hat S_n$, which is a tropicalization of the rational maps introduced by two of the authors. We study the soliton solutions
Autor:
Pavlo Pylyavskyy, Jed Yang
Publikováno v:
Pacific Journal of Mathematics. 303:703-727
Knutson, Tao, and Woodward formulated a Littlewood-Richardson rule for the cohomology ring of Grassmannians in terms of puzzles. Vakil and Wheeler-Zinn-Justin have found additional triangular puzzle pieces that allow one to express structure constant
Autor:
Dongkwan Kim, Pavlo Pylyavskyy
Publikováno v:
Selecta Mathematica. 27
The Stanley–Stembridge conjecture associates a symmetric function to each natural unit interval order $$\mathcal {P}$$ . In this paper, we define relations a la Knuth on the symmetric group for each $$\mathcal {P}$$ and conjecture that the associat
Publikováno v:
Publications of the Research Institute for Mathematical Sciences. 55:25-78
We define cluster $R$-matrices as sequences of mutations in triangular grid quivers on a cylinder, and show that the affine geometric $R$-matrix of symmetric power representations for the quantum affine algebra $U_q^\prime(\hat{\mathfrak{sl}}_n)$ can