We do here, however, solve that problem when the graph is restricted to

permutations of length n avoiding the pattern 312, that is,

permutations containing no three letters the first of which is the largest and the second one the smallest.

The rest of the paper is structured as follows: Section 2 presents a background about LSH and Minwise independent

permutations.

Hence the left-regular

permutations form a subgroup A(Q) of the group [G.

If the letters of the L edge word read downwards 12345 (see Rhombuses above), the transposed letters of the R edge word conform to one of 5

permutations (both the initial letter and the last letter being predetermined).

A ALL told, there are 43,252,003,274,489,856, 000 different positions or

permutations.

Keywords

Permutation, symmetric groups, palindromic

permutations, generalized Smarandache palindromic

permutations.

The equation ultimately yielded to group theory, which Livio calls the "language of symmetry," Group theory was developed by two 19th-century mathematicians, Niels Henrik Abel and Evariste Galois, both of whom managed their achievements during tragically short lives, Abel died of tuberculosis at 26 and Galois was killed in a duel at age 20, Livio devotes special attention to Galois, whose proof would create a new branch of algebra, The author also delves deep into groups and

permutations, and describes how symmetry applies to fields as diverse as physics and psychology.

Interspersed with narrative are student projects, such as cooking a Renaissance meal, viewing stars, and studying the

permutations of the roll of dice.

Ten narrative

permutations thus augment the three sentences: The black man finds it FUNNY, rather than SICK, that the woman looks scared, or it is the man waiting in the car, not the running man, who is sickened by the woman's fear, and so on.

What's frustrating about Feld's work is his unvarying method of introducing phrase after phrase and repeating each in canonic

permutations until the next motif replaces it--like watching insects going through genetically programmed routines for no apparent reason other than it's their destiny.

F: Well, I think the thing that causes that confusion is that I use different

permutations of rows.

Finally, the demonstrations in this paper are exact tests performed by total enumeration of all possible

permutations of the targets.