✦ LIBER ✦

On the Number of Even and Odd Latin Squares of Orderp+1

✍ Scribed by Arthur A Drisko

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 358 KB
Volume: 128
Category: Article
ISSN: 0001-8708
DOI: 10.1006/aima.1997.1623

No coin nor oath required. For personal study only.

✦ Synopsis

It is shown that given an odd prime p, the number of even latin squares of order p+1 is not equal to the number of odd latin squares of order p+1. This result is a special case of a conjecture of Alon and Tarsi and has implications for various other combinatorial problems, including conjectures of Rota and Dinitz. The proof counts even and odd latin squares modulo p 3 . This counting uses properties of isotopisms, cyclic neofields, and orthomorphisms of Z p .

1997 Academic Press

Conjecture 1 (Alon Tarsi, 1986). Let n be an even integer. Then =(L){0, where the sum runs over all latin squares L of order n.

📜 SIMILAR VOLUMES

On the maximum number of different order

On the maximum number of different ordered pairs of symbols in sets of latin squares

✍ Jeffrey H. Dinitz; Douglas R. Stinson 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 140 KB 👁 1 views

## Abstract In this paper, we study the problem of constructing sets of __s__ latin squares of order __m__ such that the average number of different ordered pairs obtained by superimposing two of the __s__ squares in the set is as large as possible. We solve this problem (for all __s__) when __m__

The Effect of Categorization on Balanced

The Effect of Categorization on Balanced Incomplete Blocks and Latin Squares

✍ J. C. W. Rayner; G. F. Liddell; A. J. Seyb 📂 Article 📅 1992 🏛 John Wiley and Sons 🌐 English ⚖ 670 KB

Robustness in the various analysis of variance models should be assessed with regard to all the assumptions. Here we assess the etTect of the continuity assumption. The models considered were chosen because they are in a sense fragile, and the elTects might be anticipated to be more dramatic here. W

On the spectrum of critical sets in lati

On the spectrum of critical sets in latin squares of order 2n

✍ Diane Donovan; James LeFevre; G. H. John van Rees 📂 Article 📅 2007 🏛 John Wiley and Sons 🌐 English ⚖ 197 KB 👁 1 views

## Abstract Suppose that __L__ is a latin square of order __m__ and __P__ ⊑ __L__ is a partial latin square. If __L__ is the only latin square of order __m__ which contains __P__, and no proper subset of __P__ has this property, then __P__ is a __critical set__ of __L__. The critical set spectrum p

On the crystal structure of odd–even nyl

On the crystal structure of odd–even nylons: Polymorphism of nylon 5,10

✍ P. Villaseñor; L. Franco; J. A. Subirana; J. Puiggalí 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 589 KB

The structure of nylon 5,10 has been investigated using electron microscopy and X-ray diffraction. Nylon 5,10 shows polymorphism with two different structures related to the ␥ form obtained by either solution or melt crystallization. Packing differences may be attributed to a change in the hydrogen

Bounds on the number of Hadamard designs

Bounds on the number of Hadamard designs of even order

✍ Clement Lam; Sigmund Lam; Vladimir D. Tonchev 📂 Article 📅 2001 🏛 John Wiley and Sons 🌐 English ⚖ 183 KB

## Abstract A new lower bound on the number of non‐isomorphic Hadamard symmetric designs of even order is proved. The new bound improves the bound on the number of Hadamard designs of order 2__n__ given in [12] by a factor of 8__n__ − 1 for every odd __n__ > 1, and for every even __n__ such that 4_

Studies on the odd-even effect of methyl

Studies on the odd-even effect of methylene spacers in poly(pyromellitimide-ester)s

✍ L. J. Francisca Mary; P. Kannan 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 190 KB 👁 2 views

Three series of poly(pyromellitimide-ester)s were synthesized from various N,NЈ-bis(-hydroxyalkyl)pyromellitimides (HAPMIs) by melt condensation with dicarboxylic acids, including terephthalic acid (TPA), 4,4Ј-biphenyldicarboxylic acid (BPDA), and 4,4Ј-azobenzenedicarboxylic acid (ABDA). Polymers we