Kazhdan-Lusztig Polynomials of Thagomizer Matroids
نویسنده
چکیده
We introduce thagomizer matroids and compute the Kazhdan-Lusztig polynomial of a rank n+1 thagomizer matroid by showing that the coefficient of tk is equal to the number of Dyck paths of semilength n with k long ascents. We also give a conjecture for the Sn-equivariant Kazhdan-Lusztig polynomial of a thagomizer matroid.
منابع مشابه
A Flag Whitney Number Formula for Matroid Kazhdan-Lusztig Polynomials
For a representation of a matroid the combinatorially defined Kazhdan-Lusztig polynomial computes the intersection cohomology of the associated reciprocal plane. However, these polynomials are difficult to compute and there are numerous open conjectures about their structure. For example, it is unknown whether or not the coefficients are non-negative for non-representable matroids. The main res...
متن کاملThe Kazhdan-Lusztig polynomial of a matroid
We associate to every matroid M a polynomial with integer coefficients, which we call the Kazhdan-Lusztig polynomial of M , in analogy with Kazhdan-Lusztig polynomials in representation theory. We conjecture that the coefficients are always non-negative, and we prove this conjecture for representable matroids by interpreting our polynomials as intersection cohomology Poincaré polynomials. We al...
متن کاملKazhdan-Lusztig polynomials of matroids: a survey of results and conjectures
We report on various results, conjectures, and open problems related to KazhdanLusztig polynomials of matroids. We focus on conjectures about the roots of these polynomials, all of which appear here for the first time.
متن کاملThe equivariant Kazhdan-Lusztig polynomial of a matroid
We define the equivariant Kazhdan-Lusztig polynomial of a matroid equipped with a group of symmetries, generalizing the nonequivariant case. We compute this invariant for arbitrary uniform matroids and for braid matroids of small rank.
متن کاملConfiguration spaces, FS-modules, and Kazhdan-Lusztig polynomials of braid matroids
The equivariant Kazhdan-Lusztig polynomial of a braid matroid may be interpreted as the intersection cohomology of a certain partial compactification of the configuration space of n distinct labeled points in C, regarded as a graded representation of the symmetric group Sn. We show that, in fixed cohomological degree, this sequence of representations of symmetric groups naturally admits the str...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 24 شماره
صفحات -
تاریخ انتشار 2017