I'm submitting an article to the Journal of Combinatoric. Now I need to follow these two requirements.
(1): In a paper divided into sections, it is desirable to number theorems, lemmas, definitions, corollaries, examples, etc. consecutively using double Arabic numerals. (E.g., Section 3 may start with Definition 3.1 followed by Remark 3.2 and Theorem 3.3).
(2): Mark the end of proof by ∎. The same symbol, placed at the end of a statement, indicates the absence of proof.
The paper I have currently is like the following: (1): The paper is divided into sections. However, the theorems, lemmas, definitions, corollaries, examples, etc, are numbered consecutively, which has nothing to do with the section order what so ever; (2): The end of the proof is marked by a blank ∎, not ∎.
Do you know how to accomplish these two tasks? Many thanks for your time and attention.