On double bound graphs and forbidden subposets

2006 ◽  
Vol 24 ◽  
pp. 267-271
Author(s):  
Kenjiro Ogawa ◽  
Satoshi Tagusari ◽  
Morimasa Tsuchiya
Keyword(s):  
Forbidden Subposets

scholarly journals Set families with forbidden subposets

2015 ◽  
Vol 136 ◽  
pp. 126-142 ◽  
Author(s):  
Linyuan Lu ◽  
Kevin G. Milans
Keyword(s):  
Forbidden Subposets

scholarly journals On double bound graphs and forbidden subposets

2009 ◽  
Vol 309 (22) ◽  
pp. 6353-6358 ◽  
Author(s):  
Kenjiro Ogawa ◽  
Satoshi Tagusari ◽  
Morimasa Tsuchiya
Keyword(s):  
Forbidden Subposets

scholarly journals Characterizing Subclasses of Cover-Incomparability Graphs by Forbidden Subposets

Order ◽  
2018 ◽  
Vol 36 (2) ◽  
pp. 349-358
Author(s):  
Jan Bok ◽  
Jana Maxová
Keyword(s):  
Forbidden Subposets

scholarly journals Forbidden subposets for fractional weak discrepancy at most k

2010 ◽  
Vol 31 (8) ◽  
pp. 1957-1963 ◽  
Author(s):  
Jeong-Ok Choi ◽  
Douglas B. West
Keyword(s):  
Forbidden Subposets ◽  
Weak Discrepancy

scholarly journals Hereditary Semiorders and Enumeration of Semiorders by Dimension

10.37236/8140 ◽  
2020 ◽  
Vol 27 (1) ◽  
Author(s):  
Mitchel T. Keller ◽  
Stephen J. Young
Keyword(s):  
Generating Function ◽  
Generating Functions ◽  
Interval Order ◽  
Structural Description ◽  
Interval Orders ◽  
Structural Result ◽  
Forbidden Subposets ◽  
Open Question ◽  
Ascent Sequences

In 2010, Bousquet-Mélou et al. defined sequences of nonnegative integers called ascent sequences and showed that the ascent sequences of length $n$ are in one-to-one correspondence with the interval orders, i.e., the posets not containing the poset $\mathbf{2}+\mathbf{2}$. Through the use of generating functions, this provided an answer to the longstanding open question of enumerating the (unlabeled) interval orders. A semiorder is an interval order having a representation in which all intervals have the same length. In terms of forbidden subposets, the semiorders exclude $\mathbf{2}+\mathbf{2}$ and $\mathbf{1}+\mathbf{3}$. The number of unlabeled semiorders on $n$ points has long been known to be the $n$th Catalan number. However, describing the ascent sequences that correspond to the semiorders under the bijection of Bousquet-Mélou et al. has proved difficult. In this paper, we discuss a major part of the difficulty in this area: the ascent sequence corresponding to a semiorder may have an initial subsequence that corresponds to an interval order that is not a semiorder. We define the hereditary semiorders to be those corresponding to an ascent sequence for which every initial subsequence also corresponds to a semiorder. We provide a structural result that characterizes the hereditary semiorders and use this characterization to determine the ordinary generating function for hereditary semiorders. We also use our characterization of hereditary semiorders and the characterization of semiorders of dimension $3$ given by Rabinovitch to provide a structural description of the semiorders of dimension at most $2$. From this description, we are able to determine the ordinary generating function for the semiorders of dimension at most $2$.

On upper bound graphs with forbidden subposets

2005 ◽  
Vol 22 ◽  
pp. 107-111
Author(s):  
Hiroshi Era ◽  
Kenjiro Ogawa ◽  
Satoshi Tagusari ◽  
Morimasa Tsuchiya
Keyword(s):  
Upper Bound ◽  
Forbidden Subposets

scholarly journals Note on upper bound graphs and forbidden subposets

2009 ◽  
Vol 309 (11) ◽  
pp. 3659-3663
Author(s):  
Kenjiro Ogawa ◽  
Satoshi Tagusari ◽  
Morimasa Tsuchiya
Keyword(s):  
Upper Bound ◽  
Forbidden Subposets
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