arXiv research

The concept of h-vector was introduced by H. Izumi in 1980. Recently we have obtained the Cartan connection for the Finsler space whose metric is given by Kropina change with an h-vector. In 1985, M. Matsumoto studied the theory of Finsler hypersurface. In this paper, we derive certain geometrical properties of a Finsl…

Results of R. Stanley and M. Masuda completely characterize the h-vectors of simplicial posets whose order complexes are spheres. In this paper we examine the corresponding question in the case where the order complex is a ball. Using the face rings of these posets, we develop a series of new conditions on their h-vect…

In this paper, we discuss the Finsler spaces $(M^n,L)$ and $(M^n,\,^{*}L)$, where $^{*}L(x,y)$ is obtained from $L(x,y)$ by Kropina change $^{*}L(x,y)=\frac{L^2(x,y)}{b_i(x,y)\,y^i}$ and $b^{}_{i}(x,y)$ is an $h$-vector in $(M^n,L)$. We find the necessary and sufficient condition when the Cartan connection coefficients…

The paper examines Matsumoto change and its Cartan connection equivalence.

Shellable tilings on simplicial complexes help understand their structure.

Product of shellable complexes yields shellable triangulations under tameness conditions.

We prove a number of new restrictions on the enumerative properties of homology manifolds and semi-Eulerian complexes and posets. These include a determination of the affine span of the fine $h$-vector of balanced semi-Eulerian complexes and the toric $h$-vector of semi-Eulerian posets. The lower bounds on simplicial h…

Recently we have obtained the Cartan connection for the Finsler space whose metric is given by an exponential change with an h-vector. In this paper, we discuss certain geometric properties of a Finslerian hyperspace subjected to an h-exponential change of metric.

New $f$-vectors reveal geometric Lefschetz-like decompositions of flag spheres.

In this paper we give a new characterization of the h-vector of the chromatic polynomial of a graph. We introduce reduced chromatic cohomology of a graph and show that h_i are its Betti numbers. We then discuss various combinatorial properties of these cohomologies. In particular we prove that these cohomologies depend…

Projection maps which appear in the theory of buildings and oriented matroids are closely related to the notion of shellability. This was first observed by Bj{ö}rner. In this paper, we give an axiomatic treatment of either concept and show their equivalence. We also axiomatize duality in this setting. As applications o…

We show that for a special alternating link diagram, the following three polynomials are essentially the same: a) the part of the HOMFLY polynomial that corresponds to the leading term in the Alexander polynomial; b) the $h$-vector for a triangulation of the root polytope of the Seifert graph and c) the enumerator of p…

Let G be a connected bipartite graph with color classes E and V and root polytope Q. Regarding the hypergraph (V,E) induced by G, we prove that its interior polynomial is equivalent to the Ehrhart polynomial of Q, which in turn is equivalent to the h-vector of any triangulation of Q. It follows that the interior polyno…