Special matchings and parabolic Kazhdan–Lusztig polynomials

Special matchings and Kazhdan-Lusztig polynomials

In 1979 Kazhdan and Lusztig defined, for every Coxeter group W , a family of polynomials, indexed by pairs of elements ofW , which have become known as the Kazhdan-Lusztig polynomials of W , and which have proven to be of importance in several areas of mathematics. In this paper we show that the combinatorial concept of a special matching plays a fundamental role in the computation of these pol...

On complexity of special maximum matchings constructing

For bipartite graphs the NP-completeness is proved for the problem of existence of maximum matching which removal leads to a graph with given lower(upper) bound for the cardinality of its maximum matching.

Combinatorial formulas for double parabolic R-polynomials

The well-known R-polynomials in Z[q], which appear in Hecke algebra computations, are closely related to certain modified R-polynomials in N[q] whose coefficients have simple combinatorial interpretations. We generalize this second family of polynomials, providing combinatorial interpretations for expressions arising in a much broader class of computations. In particular, we extend results of B...

S29. Special functions, orthogonal polynomials and applications

Special Curves and Postcritically Finite Polynomials

We study the postcritically finite maps within the moduli space of complex polynomial dynamical systems. We characterize rational curves in the moduli space containing an infinite number of postcritically finite maps, in terms of critical orbit relations, in two settings: (1) rational curves that are polynomially parameterized; and (2) cubic polynomials defined by a given fixed point multiplier...