A licence to crenellate mansum infra manerium suum was granted by Edward II.
"A Pair of Blue Eyes" by Thomas Hardy
And in each crenel of the wall was a cross and a chapel.
"High History of the Holy Graal" by Unknown
From this central block rose the twin towers, ancient, crenelated, and pierced with many loopholes.
"The Hound of the Baskervilles" by A. Conan Doyle
From this central block rose the twin towers, ancient, crenelated, and pierced with many loopholes.
"The Hound of the Baskervilles" by Arthur Conan Doyle
And, turning aside, she motioned Gonzaga to the crenel she abandoned.
"Love-at-Arms" by Raphael Sabatini
The crenellated towers are good for nothing but to sketch.
"Castilian Days" by John Hay
The solid old fabric has rows of crenels under the roof, which shows its warlike character.
"Cæsar or Nothing" by Pío Baroja Baroja
This inclosure is protected by crenellated walls and surrounded by a moat.
"Somerset" by G.W. Wade and J.H. Wade
Lesser barons lived in semi-fortified manors, many of which had been licensed to be embattled or crenelated.
"Our Legal Heritage, 5th Ed." by S. A. Reilly
A trumpet answered hoarsely from within and a mailed form arose from behind the crenellated parapet near the gate.
"Beatrix of Clare" by John Reed Scott
The only traces of defensive works which exist are portions of a crenellated wall of insignificant construction.
"Herzegovina" by George Arbuthnot
The crenelated, black border of the Chicchan-spot in Fig.
"Representation of Deities of the Maya Manuscripts" by Paul Schellhas
The crenelated Tower springs from the nave and transept.
"The Sunny Side of Ireland" by John O'Mahony and R. Lloyd Praeger
He leaned upon the crenelated parapet and hummed a strain of song as Gilian came up to him with a swinging step, now on the footway.
"Gilian The Dreamer" by Neil Munro
Its crenellations and turrets are military and forceful, not ornate.
"Cathedrals and Cloisters of the South of France, Volume 1" by Elise Whitlock Rose
The crenellated gable parapet rises from a string course with five sculptured masks, and has plain shields on its battlements.
"Bell's Cathedrals: The Cathedral Church of Rochester" by G. H. Palmer
In buildings, crenellated or pierced with loop-holes.
"The Sailor's Word-Book" by William Henry Smyth
The wall is some forty feet high, and along the top runs a broad path enclosed by crenellated parapets.
"A Wayfarer in China" by Elizabeth Kendall
The crenellations are omitted here, but they may be seen in place on the left.
"A History of Art in Chaldæa & Assyria, v. 1" by Georges Perrot
He came to the back of the building, where, two stories below him, a crenelated lower wall protecting the courtyard joined the main building.
"The Saracen: Land of the Infidel" by Robert Shea
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Owing to its suggestive shape, we will refer to the set of points in a simple permutation other than the isolated points in Figure 2 as the crenellation.
Enumerating indices of Schubert varieties defined by inclusions
The “isolated” (numbered) points must be present, and deﬁne the shape of the rest of the permutation, which we will call the crenellation.
Enumerating indices of Schubert varieties defined by inclusions
The crenellation can consist of arbitrarily many line segments, and each segment can contain any number of elements, but these must be placed in such a way as to avoid creating intervals.
Enumerating indices of Schubert varieties defined by inclusions
The labels A and B mark the two different types of sides of the crenellation and are referred to in the proof of Theorem 3.4.
Enumerating indices of Schubert varieties defined by inclusions
Note that the top row of dots, and the top of each crenellation are left to right maxima, while the bottom row of dots and the bottom of each crenellation are right to left minima.
Enumerating indices of Schubert varieties defined by inclusions
So that role must be played by two elements from the sides of a crenellation, and from different sides since an individual side is decreasing.
Enumerating indices of Schubert varieties defined by inclusions
Similarly, in a purported 35142 pattern, the 4 must come from a side of a crenellation.
Enumerating indices of Schubert varieties defined by inclusions
First we check that the 3 could come from the side of a crenellation.
Enumerating indices of Schubert varieties defined by inclusions
Since this is a left to right maximum it must come from an isolated point in the top group or the top of a crenellation.
Enumerating indices of Schubert varieties defined by inclusions
We divide the crenellation into blocks of three line segments at a time, as shown in Figure 3.
Enumerating indices of Schubert varieties defined by inclusions
Next, if I contains no points encoded by d, then I consists entirely of points within one line segment of the crenellation: since the repeated factors aa, bb and cc are forbidden, the only possibility is that I consists of the last point (encoded by c) from one block, and the ﬁrst point (encoded by a) from the next.
Enumerating indices of Schubert varieties defined by inclusions
By a similar argument, points encoded by d which lie above the crenellation can be inﬂated by any permutation from Av(312), and those below by any permutation in Av(231).
Enumerating indices of Schubert varieties defined by inclusions
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