# Snevily, Hunter S.

## Roller Coaster permutations ★★★

Author(s): Ahmed; Snevily

Let denote the set of all permutations of . Let and denote respectively the number of increasing and the number of decreasing sequences of contiguous numbers in . Let denote the set of subsequences of with length at least three. Let denote .

A permutation is called a Roller Coaster permutation if . Let be the set of all Roller Coaster permutations in .

Conjecture   For ,
\item If , then . \item If , then with .
Conjecture  (Odd Sum conjecture)   Given ,
\item If , then is odd for . \item If , then for all .

Keywords:

## Snevily's conjecture ★★★

Author(s): Snevily

Conjecture   Let be an abelian group of odd order and let satisfy . Then the elements of and may be ordered and so that the sums are pairwise distinct.

Keywords: addition table; latin square; transversal