Sentence examples for minimal presentation from inspiring English sources

There is also interest in finding inefficient finitely presented monoids since if we can find a minimal presentation P 0 for a monoid ℳ such that P 0 is not efficient, then we have χ ( P ′ ) ≥ χ ( P 0 ) > δ ( M ) for all presentations P ′ defining the same monoid ℳ.

Theorem 2.7 The inefficient but minimal presentation P M defined in (7) has a set of generating functions.

Let us take n as an odd prime p. Then, by Proposition 1 and Lemma 1, we get an inefficient but minimal presentation.

By taking i = 2 and k − l is an odd positive integer, we get a set of generating functions in terms of Stirling numbers for the inefficient but minimal presentation of the form as defined in (7).

Still for (n ge 4), it is known that the quotient (A_n /Z(A_n)) does satisfy Max-n and does not have any minimal presentation [35, Lemma 3.2 and Corollary 3.6].

Similarly to Corollary 1, the function p in the above corollary can be taken as the simplest (reduced) form being in the same congruence class as all other generating functions p that represent this minimal presentation.

Besides, he added, it usually does not make economic sense to move the minimal presentations of Encores! to Broadway.

As we noted in Remark 1, to study with the minimal presentations has an advantage for our aim in this paper.

Another outcome of this paper can be seen in Remarks 1 and 2. It is understood that to study efficient or minimal presentations (and so with the minimal number of generators) implies the minimal number of generating functions.

Of course, if AC/DC were as minimal in presentation as they are musically, they wouldn't be one tenth as popular, and Coachella shows that they still have a determination to entertain.

Our study results support the applicability of the Oxford classification even in IgAN patients with a minimal clinical presentation.