×

Let's log you in.

or

Don't have a StudySoup account? Create one here!

×

Create a StudySoup account

Be part of our community, it's free to join!

or

By creating an account you agree to StudySoup's terms and conditions and privacy policy

Already have a StudySoup account? Login here

ENUMERATIVE COMBINATORIC

by: Kennith Herman

9

0

2

ENUMERATIVE COMBINATORIC MA 614

Marketplace > University of Kentucky > Mathematics (M) > MA 614 > ENUMERATIVE COMBINATORIC
Kennith Herman
UK
GPA 3.54

Staff

These notes were just uploaded, and will be ready to view shortly.

Purchase these notes here, or revisit this page.

Either way, we'll remind you when they're ready :)

Get a free preview of these Notes, just enter your email below.

×
Unlock Preview

Why put in your email? Get access to more of this material and other relevant free materials for your school

COURSE
PROF.
Staff
TYPE
Class Notes
PAGES
2
WORDS
KARMA
25 ?

Popular in Mathematics (M)

This 2 page Class Notes was uploaded by Kennith Herman on Friday October 23, 2015. The Class Notes belongs to MA 614 at University of Kentucky taught by Staff in Fall. Since its upload, it has received 9 views. For similar materials see /class/228148/ma-614-university-of-kentucky in Mathematics (M) at University of Kentucky.

×

Reviews for ENUMERATIVE COMBINATORIC

×

×

What is Karma?

You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 10/23/15
Sign Reversing Involutions and Lattice Paths Because I was covering the material a little quickly on Friday I decided to write up some notes on the lattice paths Let ul 01 771 1171 7 k 1 712 10 and 772 k 171 7 The problem is to count the number of ordered pairs P1 P2 of lattice paths using only the steps E and N for which P1 goes from 711 to 771 P2 goes from 712 to 772 and P1 and P2 do not intersect Denote this set of paths by F Draw pictures for yourself We begin by considering a larger set of ordered pairs of lattice paths S P1P2 P1 goes from 711 to 7 and P2 goes from 712 to 77 for 139 77 j We sign the set S by SJr P1P2 P1u1 7 771 and P2 712 7 772 and S P1P2 P1 711 7 772 and P2 712 7 771 So EP1P2 P1P2 6 8 and EP1P2 71P1P2E ST Now de ne an involution 7139 on S as follows If P1 P2 do not intersect then set 7TP1 P2 P1 P2 a xed point If P1 P2 intersect then let q be the rst lattice point of intersection as you follow the paths Set 7TP1 P2 Pf PZ where P is obtained by following P1 from 711 to q and then following P2 from q to the end of P2 and P2 is obtained by following P2 from 712 to q and then following P1 from q to the end of P1 Draw pictures We now make the following observations 1 FCSf P All pairs of paths in SF must intersect in fact paths in S must cross so F is the set of xed points of 7139 C40 The number of paths P ul 7 771 is the same as the number of paths from 0 0 to 1171 7 k namely 4 Similarly the number of paths P 712 7 772 is the same as the number of paths from 00 to 1171 7 k namely U The number of paths P ul 7 772 is the same as the number of paths from 0 0 to k 7 171 7 k 7 1 namely 03 The number of paths P 712 7 771 is the same as the number of paths from 0 0 to k 7171 7 k 1 namely 5 Thus the number of pairs of paths in SJr 00 Similarly the number of pairs of paths in S kn 1 Therefore FZea 165 m SH 7 m 7 1 k f 1 2 1 1 2 As a consequence7 227 2 0 and so S 22 and thus the sequence yields 01 Z k 07 771 is con rmed to be log concave

×

×

BOOM! Enjoy Your Free Notes!

×

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

Why people love StudySoup

Jim McGreen Ohio University

"Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

Allison Fischer University of Alabama

"I signed up to be an Elite Notetaker with 2 of my sorority sisters this semester. We just posted our notes weekly and were each making over \$600 per month. I LOVE StudySoup!"

Steve Martinelli UC Los Angeles

"There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

Parker Thompson 500 Startups

"It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

Become an Elite Notetaker and start selling your notes online!
×

Refund Policy

STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.