Zobrazeno 1 - 10
of 110
pro vyhledávání: '"Billera, Louis J."'
We study a family of symmetric polynomials that we refer to as the Boolean product polynomials. The motivation for studying these polynomials stems from the computation of the characteristic polynomial of the real matroid spanned by the nonzero vecto
Externí odkaz:
http://arxiv.org/abs/1806.02943
We give a bijection between permutations of length 2n and certain pairs of Dyck paths with labels on the down steps. The bijection arises from a game in which two players alternate selecting from a set of 2n items: the permutation encodes the players
Externí odkaz:
http://arxiv.org/abs/1306.6744
Autor:
Billera, Louis J., Blanco, Saúl A.
In this note we give a numerical expression for the bandwidth $bw(P_{n}^{d})$ of the $d$-product of a path with $n$ edges, $P_{n}^{d}$. We prove that this bandwidth is given by the sum of certain multinomial coefficients. We also show that $bw(P_{n}^
Externí odkaz:
http://arxiv.org/abs/1209.3201
Autor:
Billera, Louis J., Nevo, Eran
We construct many nonpolytopal nonsimplicial Gorenstein* meet semi-lattices with nonnegative toric g-vector, supporting a conjecture of Stanley. These are formed as Bier spheres over the face posets of multiplexes, polytopes constructed by Bisztriczk
Externí odkaz:
http://arxiv.org/abs/1110.0739
Autor:
Billera, Louis J., Brenti, Francesco
We associate a quasisymmetric function to any Bruhat interval in a general Coxeter group. This association can be seen to be a morphism of Hopf algebras to the subalgebra of all peak functions, leading to an extension of the cd-index of convex polyto
Externí odkaz:
http://arxiv.org/abs/0710.3965
Publikováno v:
Adv. Math. 176: 248--276 (2003)
Via duality of Hopf algebras, there is a direct association between peak quasisymmetric functions and enumeration of chains in Eulerian posets. We study this association explicitly, showing that the notion of $\cd$-index, long studied in the context
Externí odkaz:
http://arxiv.org/abs/0706.3486
A new isomorphism invariant of matroids is introduced, in the form of a quasisymmetric function. This invariant (1) defines a Hopf morphism from the Hopf algebra of matroids to the quasisymmetric functions, which is surjective if one uses rational co
Externí odkaz:
http://arxiv.org/abs/math/0606646
We construct CW spheres from the lattices that arise as the closed sets of a convex closure, the meet-distributive lattices. These spheres are nearly polytopal, in the sense that their barycentric subdivisions are simplicial polytopes. The complete i
Externí odkaz:
http://arxiv.org/abs/math/0505576
Decomposable compositions, symmetric quasisymmetric functions and equality of ribbon Schur functions
Publikováno v:
Adv. Math. 204: 204--240 (2006)
We define an equivalence relation on integer compositions and show that two ribbon Schur functions are identical if and only if their defining compositions are equivalent in this sense. This equivalence is completely determined by means of a factoriz
Externí odkaz:
http://arxiv.org/abs/math/0405434
Autor:
Billera, Louis J., Hetyei, Gábor
The closure of the convex cone generated by all flag $f$-vectors of graded posets is shown to be polyhedral. In particular, we give the facet inequalities to the polar cone of all nonnegative chain-enumeration functionals on this class of posets. The
Externí odkaz:
http://arxiv.org/abs/math/9706220