scholarly journals Standard Paths in Another Composition Poset

10.37236/1829 ◽  
2004 ◽  
Vol 11 (1) ◽  
Author(s):  
Jan Snellman
Keyword(s):  
Generating Functions ◽  
Hasse Diagram ◽  
Term Orders ◽  
The Right

Bergeron, Bousquet-Mélou and Dulucq [Ann. Sci. Math. Québec 19 (1995), 139–151] enumerated paths in the Hasse diagram of the following poset: the underlying set is that of all compositions, and a composition $\mu$ covers another composition $\lambda$ if $\mu$ can be obtained from $\lambda$ by adding $1$ to one of the parts of $\lambda$, or by inserting a part of size $1$ into $\lambda$. We employ the methods they developed in order to study the same problem for the following poset, which is of interest because of its relation to non-commutative term orders : the underlying set is the same, but $\mu$ covers $\lambda$ if $\mu$ can be obtained from $\lambda$ by adding $1$ to one of the parts of $\lambda$, or by inserting a part of size $1$ at the left or at the right of $\lambda$. We calculate generating functions for standard paths of fixed width and for standard paths of height $\le 2$.

The random walk associated by the game of roulette

1981 ◽  
Vol 18 (04) ◽  
pp. 931-936
Author(s):  
James M. Hill ◽  
Chandra M. Gulati
Keyword(s):  
Random Walk ◽  
Power Series ◽  
Generating Functions ◽  
The Right ◽  
Lagrange's Theorem ◽  
Explicit Expressions

The random walk arising in the game of roulette involves an absorbing barrier at the origin; at each step either a unit displacement to the left or a fixed multiple displacement to the right can occur with probabilities q and p respectively. Using generating functions and Lagrange's theorem for the expansion of a function as a power series explicit expressions are deduced for the probabilities of the player's capital at the nth step.

scholarly journals On ther-Shifted Central Coefficients of Riordan Matrices

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Sai-nan Zheng ◽  
Sheng-liang Yang
Keyword(s):  
Generating Functions ◽  
Hitting Time ◽  
Central Column ◽  
Riordan Group ◽  
The Right

By presenting Riordan matrix as a triangle, the central coefficients are entries in the central column. Starting at the central column, ther-shifted central coefficients are entries in columnrof the right part of the triangle. This paper aims to characterize ther-shifted central coefficients of Riordan matrices. Here we will concentrate on four elements of the subgroups of the Riordan group, that is, the Bell subgroup, the associated subgroup, the derivative subgroup, and the hitting time subgroup. Some examples are presented to show how we deduce the generating functions for interesting sequences by using different means of calculating theser-shifted central coefficients. Besides, we make some extensions in the Bell subgroup.

The random walk associated by the game of roulette

1981 ◽  
Vol 18 (4) ◽  
pp. 931-936 ◽  
Author(s):  
James M. Hill ◽  
Chandra M. Gulati
Keyword(s):  
Random Walk ◽  
Power Series ◽  
Generating Functions ◽  
The Right ◽  
Lagrange's Theorem ◽  
Explicit Expressions

The random walk arising in the game of roulette involves an absorbing barrier at the origin; at each step either a unit displacement to the left or a fixed multiple displacement to the right can occur with probabilities q and p respectively. Using generating functions and Lagrange's theorem for the expansion of a function as a power series explicit expressions are deduced for the probabilities of the player's capital at the nth step.

A modified random walk in the presence of partially reflecting barriers

1976 ◽  
Vol 13 (1) ◽  
pp. 169-175 ◽  
Author(s):  
Saroj Dua ◽  
Shobha Khadilkar ◽  
Kanwar Sen
Keyword(s):  
Random Walk ◽  
Generating Functions ◽  
One Dimensional ◽  
Unit Step ◽  
The One ◽  
The Right ◽  
Reflecting Barriers

The paper deals with the one-dimensional modified random walk in the presence of partially reflecting barriers at a and –b (a, b > 0). The simple one-dimensional random walk on a line is the motion-record of a particle which may extend over (–∞, + ∞) or be restricted to a portion of it by absorbing and/or reflecting barriers. Here we introduce the possibility of a particle staying put along with its moving a unit step to the right or to the left and find the bivariate generating functions of the probabilities of a particle reaching m (0 <m <a) under different conditions.

A modified random walk in the presence of partially reflecting barriers

1976 ◽  
Vol 13 (01) ◽  
pp. 169-175
Author(s):  
Saroj Dua ◽  
Shobha Khadilkar ◽  
Kanwar Sen
Keyword(s):  
Random Walk ◽  
Generating Functions ◽  
One Dimensional ◽  
Unit Step ◽  
The One ◽  
The Right ◽  
Reflecting Barriers

The paper deals with the one-dimensional modified random walk in the presence of partially reflecting barriers at a and –b (a, b &gt; 0). The simple one-dimensional random walk on a line is the motion-record of a particle which may extend over (–∞, + ∞) or be restricted to a portion of it by absorbing and/or reflecting barriers. Here we introduce the possibility of a particle staying put along with its moving a unit step to the right or to the left and find the bivariate generating functions of the probabilities of a particle reaching m (0 &lt;m &lt;a) under different conditions.

scholarly journals A note on the random walk model arising in double diffusion

1982 ◽  
Vol 24 (2) ◽  
pp. 121-129 ◽  
Author(s):  
L. H. Liyanage ◽  
J. M. Hill ◽  
C. M. Gulati
Keyword(s):  
Random Walk ◽  
Probability Distribution ◽  
Diffusion Model ◽  
General Result ◽  
Generating Functions ◽  
Double Diffusion ◽  
Horizontal Position ◽  
Special Cases ◽  
One Step ◽  
The Right

AbstractThe discrete random walk problem for the unrestricted particle formulated in the double diffusion model given in Hill [2] is solved explicitly. In this model it is assumed that a particle moves along two distinct horizontal paths, say the upper path I and lower path 2. For i = 1, 2, when the particle is in path i, it can move at each jump in one of four possible ways, one step to the right with probability pi, one step to the left with probability qi, remains in the same position with probability ri, or exchanges paths but remains in the same horizontal position with probability si (pi + qi + ri + si = 1). Using generating functions, the probability distribution of the position of an unrestricted particle is derived. Finally some special cases are discussed to illustrate the general result.

scholarly journals On Some Features of the Problem of Solvability of Systems of Boolean Equations

2021 ◽  
pp. 18-28
Author(s):  
Vladimir Leontiev ◽  
◽  
Eduard Gordeev ◽  
Keyword(s):  
Generating Functions ◽  
Research Method ◽  
Number Of Solutions ◽  
Right Hand ◽  
Special Cases ◽  
Subsequent Application ◽  
Minimum Number ◽  
Covering Set ◽  
The Right

The purpose of the article is to present new results on combinatorial characteristics of systems of Boolean equations, on which such properties of systems as compatibility, solvability, number of solutions and a number of others depend. The research method is the reduction of applied problems to combinatorial models with the subsequent application of classical methods of combinatorics: the method of generating functions, the method of coefficients, methods for obtaining asymptotics, etc. Obtained result. In this paper, we obtain results concerning the solvability of systems of Boolean equations. The complexity of the problem of “ transformation” of an incompatible system into a joint one is analyzed. An approach to solving the problem of separating the minimum number of joint subsystems from an incompatible system is described and justified. The problem is reduced to the problem of finding the minimum covering set. The system compatibility criterion is obtained. Using the method of coefficients, formulas for finding and estimating the number of solutions for parameterizing the problem on the right-hand sides of equations are derived. The maximum of this number is also investigated depending on the parameter. Formulas for the number of solutions for two special cases are obtained: with a restriction on the number of equations and on the size of the problem parameters

Investor-State Dispute Settlement under NAFTA Chapter 11: The Shape of Things to Come?

1998 ◽  
Vol 35 ◽  
pp. 263-290
Author(s):  
J. Anthony VanDuzer
Keyword(s):  
Free Trade Agreement ◽  
Dispute Settlement ◽  
Trade Agreement ◽  
Minimum Standards ◽  
The North ◽  
State Behaviour ◽  
Nafta Chapter 11 ◽  
To Come ◽  
The Right

SummaryRecently, there has been a proliferation of international agreements imposing minimum standards on states in respect of their treatment of foreign investors and allowing investors to initiate dispute settlement proceedings where a state violates these standards. Of greatest significance to Canada is Chapter 11 of the North American Free Trade Agreement, which provides both standards for state behaviour and the right to initiate binding arbitration. Since 1996, four cases have been brought under Chapter 11. This note describes the Chapter 11 process and suggests some of the issues that may arise as it is increasingly resorted to by investors.

What face familiarity feelings say about the lateralization of specific entities within the core system

2019 ◽  
Vol 42 ◽  
Author(s):  
Guido Gainotti
Keyword(s):  
Temporal Lobe ◽  
Memory System ◽  
Core System ◽  
The Core ◽  
Memory Traces ◽  
Specific Memory ◽  
Target Article ◽  
Temporal Structures ◽  
The Right

Abstract The target article carefully describes the memory system, centered on the temporal lobe that builds specific memory traces. It does not, however, mention the laterality effects that exist within this system. This commentary briefly surveys evidence showing that clear asymmetries exist within the temporal lobe structures subserving the core system and that the right temporal structures mainly underpin face familiarity feelings.

Sign in / Sign up

Export Citation Format

Share Document