166 research outputs found
A survey of subdivisions and local -vectors
The enumerative theory of simplicial subdivisions (triangulations) of
simplicial complexes was developed by Stanley in order to understand the effect
of such subdivisions on the -vector of a simplicial complex. A key role
there is played by the concept of a local -vector. This paper surveys some
of the highlights of this theory and some recent developments, concerning
subdivisions of flag homology spheres and their -vectors. Several
interesting examples and open problems are discussed.Comment: 13 pages, 3 figures; minor changes and update
Some Remarks on Realization of Simplicial Algebras in Cat
In this paper we discuss why the passage from simplicial algebras over a Cat
operad to algebras over that operad involves apparently unavoidable
technicalities.Comment: 16 page
Binomial Eulerian polynomials for colored permutations
Binomial Eulerian polynomials first appeared in work of Postnikov, Reiner and
Williams on the face enumeration of generalized permutohedra. They are
-positive (in particular, palindromic and unimodal) polynomials which
can be interpreted as -polynomials of certain flag simplicial polytopes and
which admit interesting Schur -positive symmetric function
generalizations. This paper introduces analogues of these polynomials for
-colored permutations with similar properties and uncovers some new
instances of equivariant -positivity in geometric combinatorics.Comment: Final version; minor change
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