# Combinatorics: A Problem Oriented Approach by Daniel A. Marcus

By Daniel A. Marcus

This ebook teaches the artwork of enumeration, or counting, by way of prime the reader via a sequence of conscientiously selected difficulties which are prepared strategically to introduce recommendations in a logical order and in a provocative means. it truly is equipped in 8 sections, the 1st 4 of which disguise the elemental combinatorial entities of strings, mixtures, distributions, and walls. The final 4 disguise the targeted counting equipment of inclusion and exclusion, recurrence family members, producing capabilities, and the equipment of Pуlya and Redfield that may be characterised as "counting modulo symmetry. the original layout combines gains of a standard textbook with these of an issue booklet. the subject material is gifted via a chain of roughly 250 difficulties, with connecting textual content the place applicable, and is supplemented by means of nearly two hundred extra difficulties for homework assignments. Many functions to chance are integrated in the course of the publication. whereas meant essentially to be used because the textual content for a college-level direction taken via arithmetic, machine technology, and engineering scholars, the e-book is appropriate in addition for a basic schooling path at a great liberal arts collage, or for self examine.

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Extra resources for Combinatorics: A Problem Oriented Approach

Example text

Compressed equality checking can be solved in polynomial time. In Sect. 3 we give an outline of the currently fastest (and probably also simplest) algorithm for compressed equality checking, which is due to Je˙z [17]. In Sect. 4, we sketch a new approach from [22] that yields a randomized parallel algorithm for compressed equality checking. 3 Sequential Algorithms The polynomial time compressed equality checking algorithms of Hirshfeld et al. [15, 16] and Plandowski [31] use combinatorial properties of strings, in particular the periodicity lemma of Fine and Wilf [9].

Theor. Comput. Sci. 464, 48–71 (2012) 6. : Streams are forever. Bull. EATCS 109, 70–106 (2013) 7. : Invitation to mathematics. Princeton University Press (1992) 8. : The upper semi-lattice of degrees of recursive unsolvability. Ann. Math. 59(3), 379–407 (1954) 9. : Classical Recursion Theory. Studies in logic and the foundations of mathematics. North-Holland, Amsterdam (1999) 10. : Degrees of finite-state transformability. Inf. Control 24(2), 144–154 (1974) 11. : Elements of Automata Theory. Cambridge (2003) 12.

Two words u, v are k-abelian equivalents if every word of length at most k occurs as a factor in u as many times as in v. A word is strongly k-abelian nthpower if it is k-abelian equivalent to a nth-power. In WORDS 2013, Mari Huova and Aleksi Saarela prove that strongly k-abelian nth-powers are unavoidable on any alphabet. - Pattern avoidance by palindromes was the subject of the talk from Inna A. Mikhailova and Mikhail Volkov, in WORDS 2007. e. φ2 = id, φ(uv) = φ(v)φ(u)) and the pseudopalindromic closure of a word w is the shortest pseudopalindrome having w as a preﬁx.