The Kazhdan–Lusztig polynomial of a matroid
نویسندگان
چکیده
منابع مشابه
The Tutte polynomial of a ported matroid
Las Vergnas’ generalizations of the Tutte polynomial are studied as follows. The theory of Tutte-Grothendieck matroid invariantsfis modified so the Tutte decomposition ,f(M) =f(M\e) +f( M/e) is applied only when e $ P (and e is neither a loop nor an isthmus) where P is a distinguished set of points called ports. The resulting “P-ported” Tutte polynomial tp has variables I, w; q,, qZ, . . . . qm...
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We introduce the Z-polynomial of a matroid, which we define in terms of the Kazhdan-Lusztig polynomial. We then exploit a symmetry of the Z-polynomial to derive a new recursion for Kazhdan-Lusztig coefficients. We solve this recursion, obtaining a closed formula for Kazhdan-Lusztig coefficients as alternating sums of multi-indexed Whitney numbers. For realizable matroids, we give a cohomologica...
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...
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15 صفحه اولIrreducibility of the Tutte Polynomial of a Connected Matroid
We solve in the affirmative a conjecture of Brylawski, namely that the Tutte polynomial of a connected matroid is irreducible over the integers. If M is a matroid over a set E, then its Tutte polynomial is defined as T(M; x, y)= C A ı E (x − 1) r(E) − r(A) (y − 1) | A | − r(A) , where r(A) is the rank of A in M. This polynomial is an important invariant as it contains much information on the ma...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2016
ISSN: 0001-8708
DOI: 10.1016/j.aim.2016.05.005