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- Collection:
- Clark Atlanta University Faculty Publications
- Title:
- A Simple Proof for a Forbidden Subposet Problem
- Creator:
- Walker, Shanise, Clark Atlanta University
- Date of Original:
- 2020-01
- Subject:
- Degrees, Academic
Dissertations, Academic - Location:
- United States, Georgia, Fulton County, Atlanta, 33.749, -84.38798
- Medium:
- articles
- Type:
- Text
- Format:
- application/pdf
- Description:
- The posetYk,2consists ofk+ 2 distinct elementsx1,x2, . . . ,xk,y1,y2, suchthatx16x26. . .6xk6y1,y2. The posetY?k,2is the dual poset ofYk,2.The sum of theklargest binomial coefficients of ordernis denoted by ?(n, k).Let La](n,{Yk,2, Y?k,2}) be the size of the largest familyF ?2[n]that containsneitherYk,2norY?k,2as an induced subposet. Methuku and Tompkins proved thatLa](n,{Y2,2, Y?2,2}) = ?(n,2) forn>3 and conjectured the generalization that ifk>2 is an integer andn>k+1, then La](n,{Yk,2, Y?k,2}) = ?(n, k). On the other hand,it is known that La](n, Yk,2) and La](n, Y?k,2) are both strictly greater than ?(n, k).In this paper, we introduce a simple approach, motivated by discharging, to provethis conjecture.
- Metadata URL:
- http://hdl.handle.net/20.500.12322/cau.ir:2020_walker_shanise
- IIIF manifest:
- []
- Original Collection:
- The Electronic Journal of Combinatorics
- Holding Institution:
- Atlanta University Center Robert W. Woodruff Library
- Rights: