FUNCTION: IsYama - test whether the argument is a Yamanouchi word

CALLING SEQUENCE:

IsYama(expr)

TYP[IsYama](expr)

PARAMETERS:

expr = any expression

SYNOPSIS:

• The IsYama function tests whether expr is a Yamanouchi word on the alphabet of integers. By default, it tests whether expr is a left Yamanouchi word.

• IsYama(w) = IsYama(w, 'left') but one can test whether w is a right Yamanouchi word by using IsYama(w, 'right').

• We recall that a word is said to be a left Yamanouchi one if and only if all its left subwords are such that #1 >= #2 >= #3 >= ... where #i denotes the number of ith letter (first letter is the smallest integer appearing in the word). A right Yamanouchi word is obtained by replacing left by right in the previous definition.

• Whenever there is a conflict between the function name IsYama and another name used in the same session, use the long form TYP['IsYama'].

EXAMPLES:

> with(TYP):
> IsYama(w[2,1]);
 
                                     false
 
> IsYama(w[-2,-1]);
 
                                      true
 
> IsYama(w[4,3,4,4,3,3,2,1,2,2,1,1], 'right');
 
                                      true