We generalize Björner and Stanley’s poset of compositions to m-colored compositions. Their work draws many analogies between their (1-colored) composition poset and Young’s lattice of partitions, including links to (quasi-)symmetric functions and representation theory. Here we show that many of these analogies hold for any number of colors. While many of the proofs for Björner and Stanley’s pos...

In order to evaluate the creditworthiness of various countries, a learning model is induced from the 1998 S&P country risk ratings, using the 1998 values of nine economic and three political indicators. This learning model allows the construction of a partially ordered set describing the relative superiority of countries on the basis of their creditworthiness, and it is shown that the Condorcet...

The symmetric group S(n) is partially ordered by Bruhat order. This order is extended by L. Renner to the set of partial injective functions of {1, 2, . . . , n} (see, Linear Algebraic Monoids, Springer, 2005). This poset is investigated by M. Fortin in his paper The MacNeille Completion of the Poset of Partial Injective Functions [Electron. J. Combin., 15, R62, 2008]. In this paper we show tha...

We provide a method to construct a type of orthomodular structure known as an orthoalgebra from the direct product decompositions of an object in a category that has finite products and whose ternary product diagrams give rise to certain pushouts. This generalizes a method to construct an orthomodular poset from the direct product decompositions of familiar mathematical structures such as non-e...


 We construct a family of shellings for the canonical triangulation order polytope zig-zag poset. This gives new combinatorial interpretation coefficients in numerator Ehrhart series this terms swap statistic on alternating permutations. also offer an alternate proof result using techniques rank selection. Finally, we show that sequence is symmetric and unimodal.

A finite poset is an angle order if its points can be mapped into angular regions in the plane so that x precedes y in the poset precisely when the region for x is properly included in the region for y. We show that all posets of dimension four or less are angle orders, all interval orders are angle orders, and that some angle orders must have an angular region less than 180” (or more than 180”...

In this work, from the category sight, we provide a generalization for the real interval theory. This generalization allows us to study generic properties of data which are “intervals” of another data, providing a categorical foundation of intervals as a parametric data type. In doing so we obtain some properties which holds for real intervals, complex intervals, interval vectors, interval matr...

Young’s lattice is a partial order on integer partitions whose saturated chains correspond to standard Young tableaux, one type of combinatorial object that generates the Schur basis for symmetric functions. Generalizing lattice, we introduce new weak compositions call key poset. Saturated in this poset objects generate polynomials, nonsymmetric polynomial generalization basis. skew functions, ...

Birational rowmotion is a discrete dynamical system on the set of all positive real-valued functions finite poset, which birational lift combinatorial order ideals. It known that for minuscule poset has equal to Coxeter number, and exhibits file homomesy phenomenon refined ideal cardinality statistics. In this paper we generalize these results setting. Moreover, as generalization promotion prod...

Upper homogeneous finite type (upho) posets are a large class of partially ordered sets with the property that principal order filter at every vertex is isomorphic to whole poset. Well-known examples include k-ary trees, grid graphs, and Stern Very little known about upho in general. In this paper, we construct Schur-positive Ehrenborg quasisymmetric functions, whose rank-generating functions h...