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NationMaster - Encyclopedia: Pigeonhole principle (via CobWeb/3.1 planetlab2.cs.umd.edu)   (Site not responding. Last check: 2007-10-21) The pigeonhole principle is an example of a counting argument which can be applied to many formal problems, including ones involving infinite sets that cannot be put into one-to-one correspondence. If we assign a pigeonhole for each number of hairs on a head, and assign people to the pigeonhole with their number of hairs on it, there must be at least two people with the same number of hairs on their heads. If we assign a pigeonhole for each number of hairs on a head, and assign people to the pigeonhole with their number of hairs on it, there must be two people with the same number of hairs on their heads. www.nationmaster.com.cob-web.org:8888 /encyclopedia/Pigeonhole-principle   (1622 words)

PlanetMath: proof of pigeonhole principle Since the pigeonhole principle is the contrapositive of the proven statement, it follows that the pigeonhole principle holds. Cross-references: contrapositive, pigeonhole principle, surjective, injective, finite, bijection This is version 4 of proof of pigeonhole principle, born on 2003-03-14, modified 2006-10-09. planetmath.org /encyclopedia/ProofOfPigeonholePrinciple.html   (92 words)

The Puzzlers' Pigeonhole The proof makes use of the Pigeonhole Principle: If n objects are distributed between fewer than n boxes, at least one box must contain at least two of the objects. It follows from Dirichlet's box principle, that in any permutation of 10 distinct numbers there exists an increasing subsequence of at least 4 numbers or a decreasing subsequence of at least 4 numbers. Dirichlet's box principle asserts that if n objects are put into m boxes, some box must contain at least ceil(n/m) objects, some box must contain at most floor(n/m). www.maa.org /editorial/knot/pigeonhole.html   (1082 words)

Pigeonhole Principle The Pigeonhole Principle admits several useful and almost as simple extensions. Therefore, by the Pigeonhole Principle, if one selects more than n numbers from the set, two are liable to belong to the same pair that differ by n. Another application of the Pigeonhole Principle can be found on the shredding the torus page. www.cut-the-knot.org /do_you_know/pigeon.shtml   (1825 words)

CSC 4170 The Pigeonhole Principle   (Site not responding. Last check: 2007-10-21) pigeonhole principle: if n objects are put into m containers, where n > m, then at least one container must hold more than one object. The pigeonhole can be used to prove that certain infinite languages are not regular. By the pigeonhole principle, there must be distinct values of i and j such that a www.seas.upenn.edu /~cit596/notes/dave/pumping1.html   (168 words)

Making Mathematics: Mathematics Tools: Pigeonhole Principle The &#147;pigeon”; version of the pigeonhole principle states that if there are h holes and p pigeons in the holes and h < p, then there must be at least two pigeons in one hole. That is, if there is a mapping between two finite sets of unequal size, then at least one element in the smaller set must be paired with more than one element in the larger set. For practice applying this principle in different situations, see Pigeonhole Principle, The Pigeon Hole Principle, and The Pigeon Hole Principle 2. www2.edc.org /makingmath/mathtools/pigeonhole/pigeonhole.asp   (175 words)

[No title]   (Site not responding. Last check: 2007-10-21) Here pigeonhole number "i" correspond to "has i acquaintances", and the letters we are distributing among those pigeonholes are the number of acquaintances that this or that person has. Therefore there is a pigeonhole with at least two letters, i.e., there is a count of acquaintances that has at least two persons associated with it. Other problems follow where the pigeonhole principle is the key to solving the problem. www.mines.edu /fs_home/dlarue/putnam/news/news-v5.5.html   (682 words)

The Pigeonhole Principle   (Site not responding. Last check: 2007-10-21) The name "pigeonhole Principle" was coined when this counting argument was aplied to pigeons, as they occupied a set of protected havens (pigeonholes). A parity argument combined with the pigeonhole principle proves the result. Since 9 points were selected, two have the same parity combination by the pigeonhole principle. www.mathreference.com /set,pigeon.html   (197 words)

Chris Pollett > Publications, Reviews, and Talks   (Site not responding. Last check: 2007-10-21) These principles are interesting because of their close connection to the provability of circuit lower bounds, and hence the P versus NP question, in weak systems of arithmetic. in strength, the multifunction weak pigeonhole principle for quasi-log iterated p-time relations is equivalent to circuit lower bounds for quasi-log iterated p-size circuits. Circuit Principles, The Weak Pigeonhole Principle, and RSA. www.mathcs.sjsu.edu /faculty/pollett/papers/index.shtml   (3364 words)

[No title] n, then there is no injection f:[m]’![n]. Why? Think of the elements of [n] as pigeonholes and the elements of [m] as pigeons. A more general Pigeonhole Principle: If m pigeons roost in n pigeonholes, then at least one pigeonhole has at least ceil(m/n) pigeons, where ceil(x) is the ceiling function. If each of n pigeonholes has fewer then m/n pigeons, then the total number of pigeons is less than n(m/n)=m. Another generalization The book’s theorem 8.83b is another generalization of the Pigeonhole Principle. www.ms.uky.edu /~lee/amsputma504/Lecture12.doc   (1120 words)

hw13ans We are given seven integers, so by the pigeonhole principle, there must be two integers in the set of seven that map to the same remainder. However, we are given seven integers, so the pigeonhole principle cannot be applied. By the pigeonhole principle, if we pick six integers between 1 and 10, there must be at least one even integer and one odd integer. www.cs.umd.edu /class/fall2003/cmsc250/hw/hw13ans   (889 words)

Pigeonhole principle Thus if 5 integers from A are chosen, then by the pigeonhole principle, two must be from the same subset. If you're familiar with what the pigeonhole principle is used for, you'll see why this quality is important to realise, and what that means about the set of values. The answer is no. This is a case where the pigeonhole principle does not apply; the number of pigeons is not larger than the number of pigeonholes. www.physicsforums.com /showthread.php?p=1146602#post1146602   (1083 words)

University of Connecticut - Department of Mathematics   (Site not responding. Last check: 2007-10-21) Abstract: The weak pigeonhole principle (WPHP) states that there is no injective function from a set of size $n^2$ to a set of size~$n$, or dually, that there is no surjective function from the smaller set to the larger one. If the weak pigeonhole principle for polynomial-time computable functions is provable at the first level of the bounded arithmetic hierarchy $S_2^1$ (probably the most important level from the standpoint of computational complexity), then the RSA cryptosystem is insecure, so even if it is provable, it is (hopefully!) difficult to find the proof. Then I will present a specific function algebra for which a variant of the weak pigeonhole principle can be proved in $S_2^1$. www.math.uconn.edu /seminars/logic.php?rendition=printerfriendly   (399 words)

Pigeonhole Principle   (Site not responding. Last check: 2007-10-21) The Party problem Prove that at any party with six people, there must be a group of three who all know each other, or a group of three who all don't know each other (a clique or an anti-clique, respectively). It is assumed that "knowing" is symmetric, that is, if X knows Y, then Y knows X. [This is not actually a pigeonhole problem, but is part of the larger subject of Ramsey theory. The argument required is more of a case analysis, unlike pigeonhole proofs. www.employees.csbsju.edu /dmolnar/ps/114/basicpigeonhole.html   (657 words)

The Pigeon Hole Principle   (Site not responding. Last check: 2007-10-21) The so called pigeon hole principle is nothing more than the obvious remark: if you have fewer pigeon holes than pigeons and you put every pigeon in a pigeon hole, then there must result at least one pigeon hole with more than one pigeon. If a city has 10,000 different telephone lines numbered by 4-digit numbers and more than half of the telephone lines are in the downtown, then there are two telephone numbers in the downtown whose sum is again the number of a downtown telephone line. If there are 6 people at a party, then either 3 of them knew each other before the party or 3 of them were complete strangers before the party. zimmer.csufresno.edu /~larryc/proofs/proofs.pigeonhole.html   (273 words)

Pigeonhole Principle The last thing that I want to talk about is something called the pigeonhole principle. The pigeonhole principle states that if there are more pigeons then there are holes, then there must be at least one hole with at least two pigeons. How many students must be in a class to guarantee that at least two students receive the same score on the fianl exam if it is graded from 0 to 100 (102, since there are 101 scores). www.cs.uni.edu /~schafer/courses/080/sessions/s17.htm   (399 words)

Maggie Johnson________Handout #13 Pigeonhole Principle states that if there are more pigeons than pigeonholes, then there must be at least one pigeonhole with at least two pigeons in it. The Pigeonhole Principle: If k+1 or more objects are placed in k boxes, then there is at least one box containing two or more of the objects. The Generalized Pigeonhole Principle: If N objects are placed in k boxes, then there is at least one box containing at least cse.stanford.edu /class/cs103a/h31Comb.htm   (3745 words)

PigeonholePrinciple - PineWiki The pigeonhole principle says that if you put m pigeons in n < m holes, some hole gets more than one pigeon. From the pigeonhole principle we have that n <= m and m <= n and thus n = m. Note that this is a pure existence proof: it provides no guidance for finding this pair, and indeed the winning pair or pairs may change from moment to moment as students grow, shrink, slouch, get haircuts, etc. pine.cs.yale.edu /pinewiki/PigeonholePrinciple   (502 words)

INI : Abstracts : LAAW04 : When can $S^1_2$ prove the weak pigeonhole principle?   (Site not responding. Last check: 2007-10-21) It is well known result of Krajicek and Pudlak that if $S^1_2$ could prove the injective weak pigeonhole principle for every polynomial time function then RSA would not be secure. In this talk, we will consider function algebras based on a common characterization of the polynomial time functions where we slightly modify the initial functions and further restrict the amount of allowable recursion. We will then argue that $S^1_2$ can prove the surjective weak pigeonhole principle for functions in this algebra. www.newton.cam.ac.uk /programmes/LAA/Abstract4/pollett.html   (103 words)

The Quantum Pontiff » Pigeons, Discrete Log, and Entropy   (Site not responding. Last check: 2007-10-21) The pigeon hole principle states that if you put m pigeons into n<m holes, then there are at least two pigeons in one hole. Thus by the pigeon hole principle there must be two distinct subsets (two pigeons) whose product is the same. The second of these should be familiar from the class NP, and the first of these is what you’re doing when you go beyond decision problems and actually want to find a solution. dabacon.org /pontiff/?p=927   (1025 words)

hofprints - Graphs and pigeonholes   (Site not responding. Last check: 2007-10-21) Sometimes the pigeonhole principle (PHP) is used to prove a result in graph theory. The following is a famous, well-known example: (Ramsey's Theorem) If the edges of a K6 are colored with red and blue then there is a K3 subgraph which is either all red or all blue. There are many other elegant applications of the pigeonhole principle. hofprints.hofstra.edu /32   (112 words)

pigeonhole - OneLook Dictionary Search Pigeonhole : Online Plain Text English Dictionary [home, info] Phrases that include pigeonhole: example of pigeonhole principle, pigeonhole sort, pigeonhole checker, pigeonhole communication, pigeonhole messagebox, more... Words similar to pigeonhole: cubbyhole, pigeonholed, pigeonholer, pigeonholing, stamp, stereotype, compartmentalize, file, sort, more... www.onelook.com /?w=pigeonhole   (209 words)

ECCC Report TR01-055 and related Papers Improved Resolution Lower Bounds for the Weak Pigeonhole Principle Abstract: Recently, Raz established exponential lower bounds on the size of resolution proofs of the weak pigeonhole principle. You may contribute to the discussion of this ECCC Report; see the detailed instructions. eccc.hpi-web.de /eccc-reports/2001/TR01-055/index.html   (169 words)

Pigeonhole Principle He was proud that his dream of being a mathematician was not a total loss; he has at least one published paper now, something few mathematicians can claim. Speaking of sequences, there is a standard pigeonhole problem: Given any sequence of mn+1 real numbers, some subsequence of (m+1) numbers is increasing or some subsequence of (n+1) numbers is decreasing. www.cut-the-knot.org /pigeonhole/group.shtml   (544 words)

[No title] Thus we can conclude that in a group of six people there are either three mutual friends or three mutual enemies. ¡tz '€ €€€©€€€€s€ ó> Ÿ¨"Inverting the Pigeonhole PrincipleŸ ¨ðSo far we have seen that the pigeonhole principle allows us to make statements about situations where there are more elements than groups. ¡t{ '€ €€€ª€€€€s€ ó> Ÿ¨"Inverting the Pigeonhole PrincipleŸ ¨ìSo far we have seen that the pigeonhole principle allows us to make statements about situations where there are more elements than groups. eksl-www.cs.umass.edu /~bburns/cs250/Lecture20.ppt   (416 words)

ECCC Report TR01-021 and related Papers   (Site not responding. Last check: 2007-10-21) Resolution Lower Bounds for the Weak Pigeonhole Principle Abstract: We prove that any Resolution proof for the weak pigeon hole principle, with $n$ holes and any number of pigeons, is of length $Omega(2^{n^{epsilon}})$, (for some global constant $epsilon > 0$). Revision 1 of ECCC Report TR01-021, accepted on Feb 03, 2002. eccc.hpi-web.de /eccc-reports/2001/TR01-021/index.html   (89 words)

Practice problems for pigeonhole principle   (Site not responding. Last check: 2007-10-21) Here are some problems to practice the pigeonhole principle. I encourage you to post your answers on discuss to get feedback from other students on whether you've answered correctly. What is the minimum number of students so that at least 2 are guaranteed to have the same first and last name? www.cs.sunysb.edu /~cse113/Spring01/hw/pigeon.html   (201 words)

[No title] Prove that there must be two students, A and B, such that any study group containing A also contains B. How does this generalize? State the Intermediate Pigeonhole Principle: If there are _____ pigeons in ____ pigeonholes, then there must be some hole containing at least ____ pigeons. Nine darts are thrown at the original square target. www.stolaf.edu /people/molnar/ps/pigeonhole.html   (1141 words)

Coral: Publications: Efficiency Competition through Representation Changes: Pigeonhole Principle versus Linear ...   (Site not responding. Last check: 2007-10-21) Efficiency Competition through Representation Changes: Pigeonhole Principle versus Linear Programming Relaxation. In Proceedings of KR'96, the Fifth International Conference on Principles of Knowledge Representation and Reasoning, November 1996. Generated by bib2html.pl (written by Patrick Riley) on Wed Nov 08, 2006 00:00:08 www.cs.cmu.edu /~coral/publications/b2hd-yury-KR96.html   (101 words)

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