International Journal of Scientific and Research Publications

About Us
Editorial Board

Online Publication

Review Process
Publication Ethics

Call For Papers

Call for Research Paper


Online Submission
Paper Submission Guidelines
Online Publication Charge
Print Publication Charge
How to publish research paper
Publication Certificate
Research Catalogue


Join Reviewer Panel
Reviewer Guidelines

IJSRP Publications

Print Journal


IJSRP Paper Format

Contact Us

Feedback Form
Contact Us
Site Map

IJSRP, Volume 9, Issue 1, January 2019 Edition [ISSN 2250-3153]

      M. Laisin

Abstract: The bishop polynomial on a board rotated in an angle of 〖45〗^o is considered a special case of the rook polynomial. Rook polynomials are a powerful tool in the theory of restricted permutations. It is known that the rook polynomial of any board can be computed recursively, using a cell decomposition technique of Riordan. This independent study examines counting problems of non-attacking bishop placements in the game of chess and its movements in the direction of θ=〖45 〗^o to capture pieces in the same direction as the bishop with restricted positions. In this investigation, we developed the total number of ways to arrange n bishops among m positions (m≥n) and also constructed the general formula of a generating function for bishop polynomial that decomposes into n disjoint sub-boards B_1,B_2,…B_n by using an m×n array board. Furthermore, we applied it to combinatorial problems which involve permutation with forbidden positions to construct bishop polynomials in a combinatorial way.

[Reference this Paper]   [BACK]

Ooops! It appears you don't have a PDF plugin for this barrPostingser. you can click here to download the PDF file.

Reference this Research Paper (copy & paste below code):

M. Laisin (2019); Enumerative Techniques for Bishop Polynomials Generated by a θ^o Board With an m×n Array ; International Journal of Scientific and Research Publications (IJSRP) 9(1) (ISSN: 2250-3153), DOI:



About Us
Editorial Board
Call for Paper

Call for Research Paper
Paper Status
IJSRP Paper Format
Join Us

Download e-journal
Join Forum
Invite Friends
Get Social with Us!

Copyright © 2011-2021, IJSRP Inc., All rights reserved.