### Abstract

We discuss some enumerational results relating the numbers of F(n; λ _{1}, ..., λ _{m}) and F(n; λ' _{1}, ..., λ' _{k}) frequency squares of order n. In particular, for any frequency vector (λ _{1}, ..., λ _{m}) of n, we discuss some enumerational results relating the number of F(n; λ _{1}, ..., λ _{m}) frequency squares and the number of latin squares of order n. In Section 4 we also discuss some enumera- tional results for latin rectangles.

Original language | English (US) |
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Pages (from-to) | 37-52 |

Number of pages | 16 |

Journal | Quasigroups and Related Systems |

Volume | 20 |

Issue number | 1 |

State | Published - Jun 28 2012 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory
- Discrete Mathematics and Combinatorics

### Cite this

*Quasigroups and Related Systems*,

*20*(1), 37-52.

}

*Quasigroups and Related Systems*, vol. 20, no. 1, pp. 37-52.

**Some enumerational results relating the numbers of latin and frequency squares of order n.** / Castro, Francis N.; Mullen, Gary Lee; Rubio, Ivelisse.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Some enumerational results relating the numbers of latin and frequency squares of order n

AU - Castro, Francis N.

AU - Mullen, Gary Lee

AU - Rubio, Ivelisse

PY - 2012/6/28

Y1 - 2012/6/28

N2 - We discuss some enumerational results relating the numbers of F(n; λ 1, ..., λ m) and F(n; λ' 1, ..., λ' k) frequency squares of order n. In particular, for any frequency vector (λ 1, ..., λ m) of n, we discuss some enumerational results relating the number of F(n; λ 1, ..., λ m) frequency squares and the number of latin squares of order n. In Section 4 we also discuss some enumera- tional results for latin rectangles.

AB - We discuss some enumerational results relating the numbers of F(n; λ 1, ..., λ m) and F(n; λ' 1, ..., λ' k) frequency squares of order n. In particular, for any frequency vector (λ 1, ..., λ m) of n, we discuss some enumerational results relating the number of F(n; λ 1, ..., λ m) frequency squares and the number of latin squares of order n. In Section 4 we also discuss some enumera- tional results for latin rectangles.

UR - http://www.scopus.com/inward/record.url?scp=84862687263&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84862687263&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84862687263

VL - 20

SP - 37

EP - 52

JO - Quasigroups and Related Systems

JF - Quasigroups and Related Systems

SN - 1561-2848

IS - 1

ER -