Buddha in your backpack, Generating function
Dear Sumant,
I just finished the “Buddha in your backpack” by Frenz Metcalf. I had that from local library for now more than a month. I read it in bits and pieces until today when I saw it lying on heap of other books over a computer left by Nelson’s friend in my living room. I really enjoyed that book. Frank has made the book accessible to anybody who wants to learn more about Buddhism though the focus audience is teens. It starts briefly with the Buddha life then quickly teaches the 4 noble truths and eightfold path. It touches on various topics relevant to anybody and even goes into various Buddhist traditions and sects. It even has chapter on doing meditation and links to other Buddhist websites to get connected into local Sangha. The book is very practical and written in a good humor. The way Buddhism is practiced in US is different from many other parts where it may be the primary religion. Some great Japanese Zen teachers have been instrumental in bringing Buddhism to the current stage of acceptability and growth here. I read another book which talked about “Hinduism, Buddhism and Sikhism in America”. A wonderful book which tells about the way Japanese Immigrants helped spread Buddhism here. The one core concept that is so riveting and draws many people to Buddhism is its insistence on avoiding dukkha. A pretty simple philosophy isn’t it ?
Yesterday I wanted to sleep just after updating the blog and then I was getting productive with the solutions to the Combinatorics problem. I solved 4 problems, wrote them neatly using Maple. There are two more problems I could frame in my bed in the morning while I was lingering. The one uses exponential generating function and is “A poet has a daughter and she invites n number of friends to her daughter’s birthday party. They have small circular tables and being a good host she doesn’t want any of her friend to sit alone also those table cannot sit more than 6 people in a circle. What are the possible arrangements?” It’s easy to see that this is dividing into blocks and so can be solved by using exponential generating function and I verified it. If you want to try it the solution for case n = 2,3,4,5 and 6 is 1,2,9,44 and 265. The exponential generating function is e^((2-1)!*x^2/2!+(3-1)!*x^3/3!+(4-1)!*x^4/4!+(5-1)!*x^5/3!+(6-1)!*x^6/6!). Using the series function of Maple we find the coefficient of x^n/n! to be the desired value. The other problem I am now trying to construct is where I have to use ordinary generating function where again I have a bound on each interval. Like on previous problem the size of each subset has to be between 2 and 6. I thought that the problem might be like “The poet’s daughter each day writes n lines. Each poem of her contains either 2 or 3 lines (I know it’s more weird than a Haiku). How many possible poems she will have at the end of the week is she has written n number of them?” I tried to use the ordinary generating function here thinking that each poem is a continuous set of lines so my A(x) = x^2+x^3 and B(x) = 1/(1-A(x)) but the values I am getting doesn’t agree.
I think I have some clue now to have the generating function I should know for a given value of n what are going to be its subdivisions, for example in sitting around circular table we know that if there are n people we can sit them in (n-1)! ways. The same cannot be said for my above construed example. If there are n people who many ways you can divide into group of 2 or.
Anyway I think the closest question is question 18 on page 191. The semester of a college consists of n days. In how many ways can we separate the semester into sessions if each session has to consist of at least 5 days? I want it to be changed it if each session consist of at least 2 days and no more than 3 days ?
Well enough counting for today. I better get on to Analysis study. One more thing I today completed the 12th lesson from Richard Hittleman’s wonderful book. Today’s review took me almost 1 and half hr. The feeling after doing Yoga is always great. You see your spine getting straightened.
Cheers and Regards
Sumant Sumant
I just finished the “Buddha in your backpack” by Frenz Metcalf. I had that from local library for now more than a month. I read it in bits and pieces until today when I saw it lying on heap of other books over a computer left by Nelson’s friend in my living room. I really enjoyed that book. Frank has made the book accessible to anybody who wants to learn more about Buddhism though the focus audience is teens. It starts briefly with the Buddha life then quickly teaches the 4 noble truths and eightfold path. It touches on various topics relevant to anybody and even goes into various Buddhist traditions and sects. It even has chapter on doing meditation and links to other Buddhist websites to get connected into local Sangha. The book is very practical and written in a good humor. The way Buddhism is practiced in US is different from many other parts where it may be the primary religion. Some great Japanese Zen teachers have been instrumental in bringing Buddhism to the current stage of acceptability and growth here. I read another book which talked about “Hinduism, Buddhism and Sikhism in America”. A wonderful book which tells about the way Japanese Immigrants helped spread Buddhism here. The one core concept that is so riveting and draws many people to Buddhism is its insistence on avoiding dukkha. A pretty simple philosophy isn’t it ?
Yesterday I wanted to sleep just after updating the blog and then I was getting productive with the solutions to the Combinatorics problem. I solved 4 problems, wrote them neatly using Maple. There are two more problems I could frame in my bed in the morning while I was lingering. The one uses exponential generating function and is “A poet has a daughter and she invites n number of friends to her daughter’s birthday party. They have small circular tables and being a good host she doesn’t want any of her friend to sit alone also those table cannot sit more than 6 people in a circle. What are the possible arrangements?” It’s easy to see that this is dividing into blocks and so can be solved by using exponential generating function and I verified it. If you want to try it the solution for case n = 2,3,4,5 and 6 is 1,2,9,44 and 265. The exponential generating function is e^((2-1)!*x^2/2!+(3-1)!*x^3/3!+(4-1)!*x^4/4!+(5-1)!*x^5/3!+(6-1)!*x^6/6!). Using the series function of Maple we find the coefficient of x^n/n! to be the desired value. The other problem I am now trying to construct is where I have to use ordinary generating function where again I have a bound on each interval. Like on previous problem the size of each subset has to be between 2 and 6. I thought that the problem might be like “The poet’s daughter each day writes n lines. Each poem of her contains either 2 or 3 lines (I know it’s more weird than a Haiku). How many possible poems she will have at the end of the week is she has written n number of them?” I tried to use the ordinary generating function here thinking that each poem is a continuous set of lines so my A(x) = x^2+x^3 and B(x) = 1/(1-A(x)) but the values I am getting doesn’t agree.
I think I have some clue now to have the generating function I should know for a given value of n what are going to be its subdivisions, for example in sitting around circular table we know that if there are n people we can sit them in (n-1)! ways. The same cannot be said for my above construed example. If there are n people who many ways you can divide into group of 2 or.
Anyway I think the closest question is question 18 on page 191. The semester of a college consists of n days. In how many ways can we separate the semester into sessions if each session has to consist of at least 5 days? I want it to be changed it if each session consist of at least 2 days and no more than 3 days ?
Well enough counting for today. I better get on to Analysis study. One more thing I today completed the 12th lesson from Richard Hittleman’s wonderful book. Today’s review took me almost 1 and half hr. The feeling after doing Yoga is always great. You see your spine getting straightened.
Cheers and Regards
Sumant Sumant
posted by Sumant at 11:00 PM
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