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Publication# On the Number of Containments in P-free Families

Abstract

A subfamily {F-1, F-2, ..., F-vertical bar P vertical bar} subset of F is a copy of the poset P if there exists a bijection i : P -> {F-1, F-2, ..., F-vertical bar P vertical bar}, such that p k, then this number is of the order Theta(Pi(k+1)(i=1) ((li-1)(li))), where l(0) = n and l(1) >= l(2) >= ... >= l(k+1) are such that n - l(1), l(1) - l(2), ..., l(k) - l(k+1), l(k+1) differ by at most one. On the other hand if h(P)

Official source

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Related concepts (1)

Number

A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers can be represented by symbols, called numerals; for example, "5" is a numeral that represents the number five. As only a relatively small number of symbols can be memorized, basic numerals are commonly organized in a numeral system, which is an organized way to represent any number.