On combinatorial type numbers related to some special numbers

2017 ◽  
Author(s):  
Yilmaz Simsek
Keyword(s):  
Combinatorial Type

Regioselective combinatorial-type synthesis, characterization, and physical properties of dendronized cellulose

Polymer ◽  
2005 ◽  
Vol 46 (21) ◽  
pp. 8947-8955 ◽  
Author(s):  
Mohammad L. Hassan ◽  
Charles N. Moorefield ◽  
Kishore Kotta ◽  
George R. Newkome
Keyword(s):  
Physical Properties ◽  
Combinatorial Type ◽  
Type Synthesis

scholarly journals Spaces of Geodesic Triangulations of Surfaces

2022 ◽  
Author(s):  
Yanwen Luo
Keyword(s):  
Homotopy Group ◽  
Convex Polygon ◽  
Euclidean Plane ◽  
Short Proof ◽  
Combinatorial Type

AbstractWe give a short proof of the contractibility of the space of geodesic triangulations with fixed combinatorial type of a convex polygon in the Euclidean plane. Moreover, for any $$n>0$$ n > 0 , we show that there exists a space of geodesic triangulations of a polygon with a triangulation, whose n-th homotopy group is not trivial.

scholarly journals A rapid screening, ‘combinatorial-type’ survey of the metalloligand chemistry of Pt2(PPh3)4(μ-S)2 using electrospray mass spectrometry

2001 ◽  
pp. 421-422 ◽  
Author(s):  
S.-W. Audi Fong ◽  
Jagadese J. Vittal ◽  
T. S. Andy Hor ◽  
William Henderson ◽  
Allen G. Oliver ◽  
...  
Keyword(s):  
Mass Spectrometry ◽  
Electrospray Mass Spectrometry ◽  
Rapid Screening ◽  
Combinatorial Type

scholarly journals Some new identities and formulas for higher-order combinatorial-type numbers and polynomials

Filomat ◽  
2020 ◽  
Vol 34 (2) ◽  
pp. 551-558
Author(s):  
Irem Kucukoglu
Keyword(s):  
Generating Functions ◽  
Functional Equations ◽  
Stirling Numbers ◽  
Higher Order ◽  
Combinatorial Type ◽  
Derivative Formulas ◽  
Cauchy Numbers ◽  
Special Numbers And Polynomials ◽  
Boole Polynomials ◽  
Changhee Numbers

The main purpose of this paper is to provide various identities and formulas for higherorder combinatorial-type numbers and polynomials with the help of generating functions and their both functional equations and derivative formulas. The results of this paper comprise some special numbers and polynomials such as the Stirling numbers of the first kind, the Cauchy numbers, the Changhee numbers, the Simsek numbers, the Peters poynomials, the Boole polynomials, the Simsek polynomials. Finally, remarks and observations on our results are given.

scholarly journals Flow Polytopes of Partitions

10.37236/8114 ◽  
2019 ◽  
Vol 26 (1) ◽  
Author(s):  
Karola Mészáros ◽  
Connor Simpson ◽  
Zoe Wellner
Keyword(s):  
Recent Progress ◽  
Combinatorial Type ◽  
Flow Polytopes ◽  
Work Breaks ◽  
Product Of Simplices ◽  
Product Formulas

Recent progress on flow polytopes indicates many interesting families with product formulas for their volume. These product formulas are all proved using analytic techniques. Our work breaks from this pattern. We define a family of closely related flow polytopes $F_{(\lambda, {\bf a})}$ for each partition shape $\lambda$ and netflow vector ${\bf a}\in Z^n_{> 0}$. In each such family, we prove that there is a polytope (the limiting one in a sense) which is a product of scaled simplices, explaining their product volumes. We also show that the combinatorial type of all polytopes in a fixed family $F_{(\lambda, {\bf a})}$ is the same. When $\lambda$ is a staircase shape and ${\bf a}$ is the all ones vector the latter results specializes to a theorem of the first author with Morales and Rhoades, which shows that the combinatorial type of the Tesler polytope is a product of simplices.

scholarly journals Graded Betti Numbers of Balanced Simplicial Complexes

2021 ◽  
Author(s):  
Martina Juhnke-Kubitzke ◽  
Lorenzo Venturello
Keyword(s):  
Polynomial Ring ◽  
Betti Numbers ◽  
Simplicial Complexes ◽  
Upper Bounds ◽  
Combinatorial Type ◽  
Homogeneous Ideal ◽  
Graded Rings ◽  
Number Of Generators ◽  
Graded Betti Numbers ◽  
Linear Syzygies

AbstractWe prove upper bounds for the graded Betti numbers of Stanley-Reisner rings of balanced simplicial complexes. Along the way we show bounds for Cohen-Macaulay graded rings S/I, where S is a polynomial ring and $I\subseteq S$ I ⊆ S is a homogeneous ideal containing a certain number of generators in degree 2, including the squares of the variables. Using similar techniques we provide upper bounds for the number of linear syzygies for Stanley-Reisner rings of balanced normal pseudomanifolds. Moreover, we compute explicitly the graded Betti numbers of cross-polytopal stacked spheres, and show that they only depend on the dimension and the number of vertices, rather than also the combinatorial type.

scholarly journals Some Combinatorial Properties of Finite Line-Systems in the Euclidean Plane

2007 ◽  
Vol 14 (4) ◽  
pp. 681-686
Author(s):  
Alexander Kharazishvili
Keyword(s):  
Lower Estimate ◽  
Euclidean Plane ◽  
Combinatorial Type ◽  
Line System ◽  
Combinatorial Properties ◽  
Finite Systems ◽  
Euler’S Formula ◽  
Finite Line ◽  
Straight Lines

Abstract We consider finite systems of straight lines in the Euclidean plane 𝐑2 with some of their combinatorial characteristics. Euler's formula is applied for obtaining results of combinatorial type for such systems. In particular, a lower estimate for the number of two-sided and three-sided domains determined by a given finite line-system in 𝐑2 is presented and it is shown that this estimate is precise in a certain sense.

scholarly journals Embedding parallelohedra into primitive cubic networks and structural automata description

2020 ◽  
Vol 76 (6) ◽  
pp. 698-712
Author(s):  
Mikhail M. Bouniaev ◽  
Sergey V. Krivovichev
Keyword(s):  
Crystalline Structure ◽  
Finite Automaton ◽  
Combinatorial Type ◽  
Deterministic Finite Automaton ◽  
Rhombic Dodecahedron ◽  
Algorithmic Model ◽  
The Given

The main goal of the paper is to contribute to the agenda of developing an algorithmic model for crystallization and measuring the complexity of crystals by constructing embeddings of 3D parallelohedra into a primitive cubic network (pcu net). It is proved that any parallelohedron P as well as tiling by P, except the rhombic dodecahedron, can be embedded into the 3D pcu net. It is proved that for the rhombic dodecahedron embedding into the 3D pcu net does not exist; however, embedding into the 4D pcu net exists. The question of how many ways the embedding of a parallelohedron can be constructed is answered. For each parallelohedron, the deterministic finite automaton is developed which models the growth of the crystalline structure with the same combinatorial type as the given parallelohedron.

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