Result: Enumeration by kernel positions
Title:
Enumeration by kernel positions
Authors:
Source:
Advances in applied mathematics (Print). 42(4):445-470
Publisher Information:
San Diego, CA: Elsevier, 2009.
Publication Year:
2009
Physical Description:
print, 18 ref
Original Material:
INIST-CNRS
Subject Terms:
Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Combinatoire. Structures ordonnées, Combinatorics. Ordered structures, Combinatoire, Combinatorics, Algèbre, Algebra, Théorie des nombres, Number theory, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Généralités, histoire et biographie, General, history and biography, Mathématiques générales, General mathematics, Combinatoire, Combinatorics, Combinatoria, Ensemble partiellement ordonné, Partially ordered set, Conjunto parcialmento ordenado, Fonction génératrice, Generating function, Función generatriz, Mathématiques appliquées, Applied mathematics, Matemáticas aplicadas, Nombre Bernoulli, Bernoulli number, Número Bernoulli, Nombre entier, Integer, Entero, Polynôme, Polynomial, Polinomio, 05XX, 11B68, 91A05, 91A46,; 91A60; Bernoulli polynomials; Degenerate Bernoullli numbers; Digamma function; Progressively finite games; Kernel position; Enumerative combinatorics; Generating functions; Newton expansion; Euler's C constant, primary 05A15; secondary 05A40
Document Type:
Academic journal
Article
File Description:
text
Language:
English
Author Affiliations:
Department of Mathematics and Statistics, University of North Carolina at Charlotte, 9201 University City Boulevard, NC 28223, United States
ISSN:
0196-8858
Rights:
Copyright 2009 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.21386165
Database:
PASCAL Archive
Further Information
We introduce a class of two-player games on posets with a rank function, in which each move of the winning strategy is unique. This allows one to enumerate the kernel positions by rank. The main example is a simple game on words in which the number of kernel positions of rank n is a signed factorial multiple of the nth Bernoulli number of the second kind. Generalizations to the degenerate Bernoulli numbers and to negative integer substitutions into the Bernoulli polynomials are developed. Using an appropriate scoring system for each function with an appropriate Newton expansion we construct a game in which the expected gain of a player equals the definite integral of the function on the interval |0,1|.