Permutations with Kazhdan-Lusztig polynomial . With an appendix by Sara Billey and Jonathan Weed.
Permutations without long decreasing subsequences and random matrices.
Persistency in the Traveling Salesman Problem on Halin graphs
For the Traveling Salesman Problem (TSP) on Halin graphs with three types of cost functions: sum, bottleneck and balanced and with arbitrary real edge costs we compute in polynomial time the persistency partition , , of the edge set E, where: = e ∈ E, e belongs to all optimum solutions, = e ∈ E, e does not belong to any optimum solution and = e ∈ E, e belongs to some but not to all optimum solutions.
Pfaffian orientation and enumeration of perfect matchings for some Cartesian products of graphs.
Pfaff's method. III: Comparison with the WZ method.
Pflasterungen des Raumes mit Pyramiden und Doppelpyramiden.
Pieri's formula for flag manifolds and Schubert polynomials
We establish the formula for multiplication by the class of a special Schubert variety in the integral cohomology ring of the flag manifold. This formula also describes the multiplication of a Schubert polynomial by either an elementary or a complete symmetric polynomial. Thus, we generalize the classical Pieri’s formula for Schur polynomials (associated to Grassmann varieties) to Schubert polynomials (associated to flag manifolds). Our primary technique is an explicit geometric description of certain...
Pilesize dynamic one-pile Nim and Beatty's theorem.
Pinning lag synchronization between two dynamical networks with non-derivative and derivative couplings
In this paper, we study lag synchronization between two dynamical networks with non-derivative and derivative couplings via pinning control. We design two types of pinning control schemes, including linear and adaptive feedback controllers. With the corresponding control algorithms, we obtain two theorems on the lag synchronization based on Schur complement and Barbalat's lemma. In addition, we obtain the domain for the linear feedback gains. Finally, we provide two numerical examples to show the...
Place-difference-value patterns: a generalization of generalized permutation and word patterns.
Placing bipartite graphs of small size II
In this paper we give all pairs of non mutually placeable (p,q)-bipartite graphs G and H such that 2 ≤ p ≤ q, e(H) ≤ p and e(G)+e(H) ≤ 2p+q-1.
Planar binary trees and perturbative calculus of observables in classical field theory
Planar decompositions and the crossing number of graphs with an excluded minor.
Planar drawings of higher-genus graphs.
Planar graphs as minimal resolutions of trivariate monomial ideals.
Planar graphs with topological constraints.
Planar graphs without 4-, 5- and 8-cycles are 3-colorable
In this paper we prove that every planar graph without 4, 5 and 8-cycles is 3-colorable.
Planar graphs without triangles adjacent to cycles of length from 3 to 9 are 3-colorable.
Planar maps as labeled mobiles.
Planar ordered sets of width two