A Rational Generating Function for Relative Divisors: 10750

2001 ◽  
Vol 108 (7) ◽  
pp. 670
Author(s):  
Leonard Smiley ◽  
David Callan ◽  
David M. Wells ◽  
Said Amghibech
Keyword(s):  
Generating Function ◽  
Rational Generating Function

scholarly journals Pattern Avoidance Classes and Subpermutations

10.37236/1957 ◽  
2005 ◽  
Vol 12 (1) ◽  
Author(s):  
M. D. Atkinson ◽  
M. M. Murphy ◽  
N. Ruškuc
Keyword(s):  
Generating Function ◽  
Structure Theorem ◽  
Pattern Avoidance ◽  
Natural Numbers ◽  
Direct Sums ◽  
Rational Generating Function

Pattern avoidance classes of permutations that cannot be expressed as unions of proper subclasses can be described as the set of subpermutations of a single bijection. In the case that this bijection is a permutation of the natural numbers a structure theorem is given. The structure theorem shows that the class is almost closed under direct sums or has a rational generating function.

A Doubly Rational Generating Function: 10493

1998 ◽  
Vol 105 (10) ◽  
pp. 956
Author(s):  
Richard P. Stanley ◽  
Christophe Reutenauer ◽  
Robin J. Chapman
Keyword(s):  
Generating Function ◽  
Rational Generating Function

scholarly journals Some Theorems on Tauber's Generalized Stirling, Lah and Bell Numbers

2019 ◽  
Vol 12 (3) ◽  
pp. 1069-1081
Author(s):  
Roberto Bagsarsa Corcino ◽  
Cristina Bordaje Corcino ◽  
Gladys Jane Rama
Keyword(s):  
Explicit Formula ◽  
Generating Function ◽  
Symmetric Function ◽  
Recurrence Relations ◽  
Function Form ◽  
Bell Numbers ◽  
Rational Generating Function

In this paper, some properties for Tauber's generalized Stirling and Lah numbers are obtained including other forms of recurrence relations, orthogonality and inverse relations, rational generating function and explicit formual in symmetric function form. Moreover, a new explicit formula is derived, which is analogous to the Qi formula.

System of thermodynamic quantities in the McMillan-Mayer solution theory

1985 ◽  
Vol 50 (4) ◽  
pp. 791-798 ◽  
Author(s):  
Vilém Kodýtek
Keyword(s):  
Free Energy ◽  
Generating Function ◽  
Simple Form ◽  
Unit Volume ◽  
Thermodynamic Quantities ◽  
Solution Theory ◽  
Pure Solvent ◽  
Second Derivatives ◽  
Definition Of ◽  
Derivatives Of

The McMillan-Mayer (MM) free energy per unit volume of solution AMM, is employed as a generating function of the MM system of thermodynamic quantities for solutions in the state of osmotic equilibrium with pure solvent. This system can be defined by replacing the quantities G, T, P, and m in the definition of the Lewis-Randall (LR) system by AMM, T, P0, and c (P0 being the pure solvent pressure). Following this way the LR to MM conversion relations for the first derivatives of the free energy are obtained in a simple form. New relations are derived for its second derivatives.

scholarly journals A General Family of q-Hypergeometric Polynomials and Associated Generating Functions

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1161
Author(s):  
Hari Mohan Srivastava ◽  
Sama Arjika
Keyword(s):  
Generating Function ◽  
Generating Functions ◽  
Hypergeometric Functions ◽  
Additional Parameter ◽  
Physical Sciences ◽  
General Family ◽  
Hypergeometric Polynomials

Basic (or q-) series and basic (or q-) polynomials, especially the basic (or q-) hypergeometric functions and the basic (or q-) hypergeometric polynomials are studied extensively and widely due mainly to their potential for applications in many areas of mathematical and physical sciences. Here, in this paper, we introduce a general family of q-hypergeometric polynomials and investigate several q-series identities such as an extended generating function and a Srivastava-Agarwal type bilinear generating function for this family of q-hypergeometric polynomials. We give a transformational identity involving generating functions for the generalized q-hypergeometric polynomials which we have introduced here. We also point out relevant connections of the various q-results, which we investigate here, with those in several related earlier works on this subject. We conclude this paper by remarking that it will be a rather trivial and inconsequential exercise to give the so-called (p,q)-variations of the q-results, which we have investigated here, because the additional parameter p is obviously redundant.

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