Zobrazeno 1 - 10
of 179
pro vyhledávání: '"Marberg, Eric"'
Autor:
Marberg, Eric
We provide a construction for the kromatic symmetric function $\overline{X}_G$ of a graph introduced by Crew, Pechenik, and Spirkl using combinatorial (linearly compact) Hopf algebras. As an application, we show that $\overline{X}_G$ has a positive e
Externí odkaz:
http://arxiv.org/abs/2312.16474
Autor:
Marberg, Eric, Tong, Kam Hung
We describe two crystal structures on set-valued decomposition tableaux. These provide the first examples of interesting "$K$-theoretic" crystals on shifted tableaux. Our first crystal is modeled on a similar construction of Monical, Pechenik, and Sc
Externí odkaz:
http://arxiv.org/abs/2312.16776
Autor:
Marberg, Eric, Tong, Kam Hung
Our previous work introduced a category of extended queer crystals, whose connected normal objects have unique highest weight elements and characters that are Schur $Q$-polynomials. The initial models for such crystals were based on semistandard shif
Externí odkaz:
http://arxiv.org/abs/2312.15409
Autor:
Marberg, Eric, Scrimshaw, Travis
This article continues our study of $P$- and $Q$-key polynomials, which are (non-symmetric) "partial" Schur $P$- and $Q$-functions as well as "shifted" versions of key polynomials. Our main results provide a crystal interpretation of $P$- and $Q$-key
Externí odkaz:
http://arxiv.org/abs/2306.00336
Autor:
Marberg, Eric, Scrimshaw, Travis
We introduce shifted analogues of key polynomials related to symplectic and orthogonal orbit closures in the complete flag variety. Our definitions are given by applying isobaric divided difference operators to the analogues of Schubert polynomials f
Externí odkaz:
http://arxiv.org/abs/2302.04226
Autor:
Marberg, Eric, Zhang, Yifeng
Publikováno v:
Ann. Comb. (2024)
The two tableaux assigned by the Robinson--Schensted correspondence are equal if and only if the input permutation is an involution, so the RS algorithm restricts to a bijection between involutions in the symmetric group and standard tableaux. Beissi
Externí odkaz:
http://arxiv.org/abs/2212.13373
Autor:
Marberg, Eric
In prior joint work with Lewis, we developed a theory of enriched set-valued $P$-partitions to construct a $K$-theoretic generalization of the Hopf algebra of peak quasisymmetric functions. Here, we situate this object in a diagram of six Hopf algebr
Externí odkaz:
http://arxiv.org/abs/2211.01092
Autor:
Lewis, Joel Brewster, Marberg, Eric
Publikováno v:
Forum of Mathematics, Sigma (2024), Vol. 12, Paper e22
The $K$-theoretic Schur $P$- and $Q$-functions $GP_\lambda$ and $GQ_\lambda$ may be concretely defined as weight generating functions for semistandard shifted set-valued tableaux. These symmetric functions are the shifted analogues of stable Grothend
Externí odkaz:
http://arxiv.org/abs/2209.03551
Autor:
Marberg, Eric, Zhang, Yifeng
Publikováno v:
J. Pure Appl. Algebra 227 (2023), 107303
A model for a finite group is a set of linear characters of subgroups that can be induced to obtain every irreducible character exactly once. A perfect model for a finite Coxeter group is a model in which the relevant subgroups are the quasiparabolic
Externí odkaz:
http://arxiv.org/abs/2201.00748
Autor:
Marberg, Eric, Tong, Kam Hung
Publikováno v:
Combinatorial Theory 3 (2023), no. 2., #6
Work of Grantcharov et al. develops a theory of abstract crystals for the queer Lie superalgebra $\mathfrak{q}_n$. Such $\mathfrak{q}_n$-crystals form a monoidal category in which the connected normal objects have unique highest weight elements and c
Externí odkaz:
http://arxiv.org/abs/2112.02848