Partitions for Semi-magic Squares of Size Three

نویسندگان

چکیده

In the theory of Clebsch-Gordan coefficients, one may recognize domain space as set weakly semi-magic squares size three. Two partitions on this are considered: a triangle-hexagon model based top lines, and orbits under finite group action. addition to giving another proof McMahon's formula, we give generating function that counts so-called trivial zeros coefficients its associated quasi-polynomial.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Semi-magic Squares and Elliptic Curves

We show that, for all odd natural numbers N , the N-torsion points on an elliptic curve may be placed in an N × N grid such that the sum of each column and each row is the point at infinity.

متن کامل

Constructing all magic squares of order three

A magic square of order n is an n by n matrix with distinct nonnegative integer entries such that every row sum, column sum, and (two) diagonal sums equals to the same number m, the magic number. Adding 1 to every entry will give us a traditional magic square of positive integers. A magic square is pure if the entries are the consecutive numbers from 0 to n − 1, and hence it has magic number 3 ...

متن کامل

Creating Semi-Magic, Magic and Extra Magic n× n Squares when n is Odd

We define a simple algorithm for creating large numbers of semi-magic n× n squares when n is odd. Special cases of the algorithm can also be used to easily create magic and extra magic (or panmagic) n× n squares when n is odd. The algorithm can also create extremely magic n × n squares when n ≥ 5 is prime. These extremely magic n × n squares have n! standard magic n-element subsets, and these n...

متن کامل

Properties of Magic Squares of Squares

A problem due to Martin LaBar is to find a 3x3 magic square with 9 distinct perfect square entries or prove that such a magic square cannot exist (LaBar [1]). This problem has been tied to various domains including arithmetic progressions, rational right triangles, and elliptic curves (Robertson [2]). However, there are some interesting properties that can be derived without ever leaving the do...

متن کامل

Magic Squares and Sudoku

We introduce a family of magic squares, called linear magic squares, and show that any parallel linear sudoku solution of sufficiently large order can be relabeled so that all of its subsquares are linear magic. As a consequence, we show that if n has prime factorization p1 1 · · · p kt t and q = min{p k j j | 1 ≤ j ≤ t}, then there is a family of q(q − 1) mutually orthogonal magic sudoku solut...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Springer proceedings in mathematics & statistics

سال: 2021

ISSN: ['2194-1009', '2194-1017']

DOI: https://doi.org/10.1007/978-3-030-67996-5_7