id	sid	tid	token	lemma	pos
zk51vd69n54	1	1	the	the	DET
zk51vd69n54	1	2	concept	concept	NOUN
zk51vd69n54	1	3	of	of	ADP
zk51vd69n54	1	4	root	root	NOUN
zk51vd69n54	1	5	systems	system	NOUN
zk51vd69n54	1	6	arises	arise	VERB
zk51vd69n54	1	7	in	in	ADP
zk51vd69n54	1	8	the	the	DET
zk51vd69n54	1	9	study	study	NOUN
zk51vd69n54	1	10	of	of	ADP
zk51vd69n54	1	11	many	many	ADJ
zk51vd69n54	1	12	mathematical	mathematical	ADJ
zk51vd69n54	1	13	areas	area	NOUN
zk51vd69n54	1	14	.	.	PUNCT
zk51vd69n54	2	1	in	in	ADP
zk51vd69n54	2	2	particular	particular	ADJ
zk51vd69n54	2	3	it	it	PRON
zk51vd69n54	2	4	is	be	AUX
zk51vd69n54	2	5	a	a	DET
zk51vd69n54	2	6	crucial	crucial	ADJ
zk51vd69n54	2	7	tool	tool	NOUN
zk51vd69n54	2	8	for	for	ADP
zk51vd69n54	2	9	understanding	understand	VERB
zk51vd69n54	2	10	coxeter	coxeter	NOUN
zk51vd69n54	2	11	groups	group	NOUN
zk51vd69n54	2	12	and	and	CCONJ
zk51vd69n54	2	13	various	various	ADJ
zk51vd69n54	2	14	groupoids	groupoid	NOUN
zk51vd69n54	2	15	which	which	PRON
zk51vd69n54	2	16	demonstrate	demonstrate	VERB
zk51vd69n54	2	17	coxeter	coxeter	NOUN
zk51vd69n54	2	18	like	like	ADP
zk51vd69n54	2	19	properties.in	properties.in	ADP
zk51vd69n54	2	20	this	this	DET
zk51vd69n54	2	21	dissertation	dissertation	NOUN
zk51vd69n54	2	22	we	we	PRON
zk51vd69n54	2	23	study	study	VERB
zk51vd69n54	2	24	matroidal	matroidal	ADJ
zk51vd69n54	2	25	properties	property	NOUN
zk51vd69n54	2	26	of	of	ADP
zk51vd69n54	2	27	various	various	ADJ
zk51vd69n54	2	28	root	root	NOUN
zk51vd69n54	2	29	systems	system	NOUN
zk51vd69n54	2	30	.	.	PUNCT
zk51vd69n54	3	1	first	first	ADV
zk51vd69n54	3	2	we	we	PRON
zk51vd69n54	3	3	consider	consider	VERB
zk51vd69n54	3	4	the	the	DET
zk51vd69n54	3	5	signed	sign	VERB
zk51vd69n54	3	6	groupoid	groupoid	NOUN
zk51vd69n54	3	7	set	set	VERB
zk51vd69n54	3	8	,	,	PUNCT
zk51vd69n54	3	9	a	a	DET
zk51vd69n54	3	10	concept	concept	NOUN
zk51vd69n54	3	11	which	which	PRON
zk51vd69n54	3	12	was	be	AUX
zk51vd69n54	3	13	developed	develop	VERB
zk51vd69n54	3	14	by	by	ADP
zk51vd69n54	3	15	dyer	dyer	NOUN
zk51vd69n54	3	16	and	and	CCONJ
zk51vd69n54	3	17	generalizes	generalize	VERB
zk51vd69n54	3	18	many	many	ADJ
zk51vd69n54	3	19	notions	notion	NOUN
zk51vd69n54	3	20	including	include	VERB
zk51vd69n54	3	21	coxeter	coxeter	NOUN
zk51vd69n54	3	22	groups	group	NOUN
zk51vd69n54	3	23	,	,	PUNCT
zk51vd69n54	3	24	coxeter	coxeter	NOUN
zk51vd69n54	3	25	groupoids	groupoid	NOUN
zk51vd69n54	3	26	and	and	CCONJ
zk51vd69n54	3	27	coxeter	coxeter	PROPN
zk51vd69n54	3	28	-	-	PUNCT
zk51vd69n54	3	29	like	like	ADJ
zk51vd69n54	3	30	groupoid	groupoid	NOUN
zk51vd69n54	3	31	studied	study	VERB
zk51vd69n54	3	32	by	by	ADP
zk51vd69n54	3	33	brink	brink	PROPN
zk51vd69n54	3	34	and	and	CCONJ
zk51vd69n54	3	35	howlett	howlett	PROPN
zk51vd69n54	3	36	.	.	PUNCT
zk51vd69n54	4	1	we	we	PRON
zk51vd69n54	4	2	show	show	VERB
zk51vd69n54	4	3	that	that	SCONJ
zk51vd69n54	4	4	the	the	DET
zk51vd69n54	4	5	finite	finite	NOUN
zk51vd69n54	4	6	,	,	PUNCT
zk51vd69n54	4	7	connected	connect	VERB
zk51vd69n54	4	8	,	,	PUNCT
zk51vd69n54	4	9	simply	simply	ADV
zk51vd69n54	4	10	connected	connect	VERB
zk51vd69n54	4	11	,	,	PUNCT
zk51vd69n54	4	12	real	real	ADJ
zk51vd69n54	4	13	,	,	PUNCT
zk51vd69n54	4	14	compressed	compressed	ADJ
zk51vd69n54	4	15	,	,	PUNCT
zk51vd69n54	4	16	principal	principal	ADJ
zk51vd69n54	4	17	,	,	PUNCT
zk51vd69n54	4	18	complete	complete	ADJ
zk51vd69n54	4	19	and	and	CCONJ
zk51vd69n54	4	20	rootoidal	rootoidal	ADJ
zk51vd69n54	4	21	signed	sign	VERB
zk51vd69n54	4	22	groupoid	groupoid	NOUN
zk51vd69n54	4	23	sets	set	NOUN
zk51vd69n54	4	24	correspond	correspond	VERB
zk51vd69n54	4	25	bijectively	bijectively	ADV
zk51vd69n54	4	26	to	to	ADP
zk51vd69n54	4	27	the	the	DET
zk51vd69n54	4	28	oriented	orient	VERB
zk51vd69n54	4	29	simplicial	simplicial	NOUN
zk51vd69n54	4	30	geometries.in	geometries.in	X
zk51vd69n54	4	31	the	the	DET
zk51vd69n54	4	32	second	second	ADJ
zk51vd69n54	4	33	part	part	NOUN
zk51vd69n54	4	34	,	,	PUNCT
zk51vd69n54	4	35	we	we	PRON
zk51vd69n54	4	36	studied	study	VERB
zk51vd69n54	4	37	the	the	DET
zk51vd69n54	4	38	closure	closure	NOUN
zk51vd69n54	4	39	operator	operator	NOUN
zk51vd69n54	4	40	and	and	CCONJ
zk51vd69n54	4	41	lattice	lattice	NOUN
zk51vd69n54	4	42	property	property	NOUN
zk51vd69n54	4	43	of	of	ADP
zk51vd69n54	4	44	the	the	DET
zk51vd69n54	4	45	root	root	NOUN
zk51vd69n54	4	46	system	system	NOUN
zk51vd69n54	4	47	of	of	ADP
zk51vd69n54	4	48	an	an	DET
zk51vd69n54	4	49	infinite	infinite	ADJ
zk51vd69n54	4	50	coxeter	coxeter	X
zk51vd69n54	4	51	group	group	NOUN
zk51vd69n54	4	52	.	.	PUNCT
zk51vd69n54	5	1	we	we	PRON
zk51vd69n54	5	2	establish	establish	VERB
zk51vd69n54	5	3	a	a	DET
zk51vd69n54	5	4	bijection	bijection	NOUN
zk51vd69n54	5	5	between	between	ADP
zk51vd69n54	5	6	the	the	DET
zk51vd69n54	5	7	infinitely	infinitely	ADV
zk51vd69n54	5	8	long	long	ADJ
zk51vd69n54	5	9	words	word	NOUN
zk51vd69n54	5	10	of	of	ADP
zk51vd69n54	5	11	an	an	DET
zk51vd69n54	5	12	affine	affine	ADJ
zk51vd69n54	5	13	weyl	weyl	NOUN
zk51vd69n54	5	14	group	group	NOUN
zk51vd69n54	5	15	and	and	CCONJ
zk51vd69n54	5	16	certain	certain	ADJ
zk51vd69n54	5	17	biclosed	biclosed	ADJ
zk51vd69n54	5	18	sets	set	NOUN
zk51vd69n54	5	19	of	of	ADP
zk51vd69n54	5	20	its	its	PRON
zk51vd69n54	5	21	positive	positive	ADJ
zk51vd69n54	5	22	system	system	NOUN
zk51vd69n54	5	23	.	.	PUNCT
zk51vd69n54	6	1	using	use	VERB
zk51vd69n54	6	2	this	this	DET
zk51vd69n54	6	3	bijection	bijection	NOUN
zk51vd69n54	6	4	,	,	PUNCT
zk51vd69n54	6	5	we	we	PRON
zk51vd69n54	6	6	show	show	VERB
zk51vd69n54	6	7	first	first	ADV
zk51vd69n54	6	8	that	that	SCONJ
zk51vd69n54	6	9	the	the	DET
zk51vd69n54	6	10	biclosed	biclosed	ADJ
zk51vd69n54	6	11	sets	set	NOUN
zk51vd69n54	6	12	in	in	ADP
zk51vd69n54	6	13	the	the	DET
zk51vd69n54	6	14	standard	standard	ADJ
zk51vd69n54	6	15	positive	positive	ADJ
zk51vd69n54	6	16	system	system	NOUN
zk51vd69n54	6	17	of	of	ADP
zk51vd69n54	6	18	rank	rank	NOUN
zk51vd69n54	6	19	3	3	NUM
zk51vd69n54	6	20	affine	affine	NOUN
zk51vd69n54	6	21	weyl	weyl	NOUN
zk51vd69n54	6	22	groups	group	NOUN
zk51vd69n54	6	23	when	when	SCONJ
zk51vd69n54	6	24	ordered	order	VERB
zk51vd69n54	6	25	by	by	ADP
zk51vd69n54	6	26	inclusion	inclusion	NOUN
zk51vd69n54	6	27	form	form	VERB
zk51vd69n54	6	28	a	a	DET
zk51vd69n54	6	29	complete	complete	ADJ
zk51vd69n54	6	30	algebraic	algebraic	ADJ
zk51vd69n54	6	31	ortholattice	ortholattice	NOUN
zk51vd69n54	6	32	and	and	CCONJ
zk51vd69n54	6	33	secondly	secondly	ADV
zk51vd69n54	6	34	that	that	SCONJ
zk51vd69n54	6	35	the	the	DET
zk51vd69n54	6	36	(	(	PUNCT
zk51vd69n54	6	37	generalized	generalized	ADJ
zk51vd69n54	6	38	)	)	PUNCT
zk51vd69n54	6	39	braid	braid	NOUN
zk51vd69n54	6	40	graphs	graph	NOUN
zk51vd69n54	6	41	of	of	ADP
zk51vd69n54	6	42	those	those	DET
zk51vd69n54	6	43	coxeter	coxeter	NOUN
zk51vd69n54	6	44	groups	group	NOUN
zk51vd69n54	6	45	are	be	AUX
zk51vd69n54	6	46	connected	connect	VERB
zk51vd69n54	6	47	,	,	PUNCT
zk51vd69n54	6	48	which	which	PRON
zk51vd69n54	6	49	can	can	AUX
zk51vd69n54	6	50	be	be	AUX
zk51vd69n54	6	51	thought	think	VERB
zk51vd69n54	6	52	as	as	ADP
zk51vd69n54	6	53	an	an	DET
zk51vd69n54	6	54	infinite	infinite	ADJ
zk51vd69n54	6	55	version	version	NOUN
zk51vd69n54	6	56	of	of	ADP
zk51vd69n54	6	57	tit	tit	PROPN
zk51vd69n54	6	58	's	's	PART
zk51vd69n54	6	59	solution	solution	NOUN
zk51vd69n54	6	60	to	to	ADP
zk51vd69n54	6	61	the	the	DET
zk51vd69n54	6	62	word	word	NOUN
zk51vd69n54	6	63	problem	problem	NOUN
zk51vd69n54	6	64	.	.	PUNCT
zk51vd69n54	7	1	finally	finally	ADV
zk51vd69n54	7	2	we	we	PRON
zk51vd69n54	7	3	investigate	investigate	VERB
zk51vd69n54	7	4	the	the	DET
zk51vd69n54	7	5	relationship	relationship	NOUN
zk51vd69n54	7	6	between	between	ADP
zk51vd69n54	7	7	infinitely	infinitely	ADV
zk51vd69n54	7	8	long	long	ADJ
zk51vd69n54	7	9	words	word	NOUN
zk51vd69n54	7	10	and	and	CCONJ
zk51vd69n54	7	11	twisted	twisted	ADJ
zk51vd69n54	7	12	weak	weak	ADJ
zk51vd69n54	7	13	orders	order	NOUN
zk51vd69n54	7	14	and	and	CCONJ
zk51vd69n54	7	15	show	show	VERB
zk51vd69n54	7	16	that	that	SCONJ
zk51vd69n54	7	17	for	for	ADP
zk51vd69n54	7	18	affine	affine	ADJ
zk51vd69n54	7	19	weyl	weyl	NOUN
zk51vd69n54	7	20	groups	group	NOUN
zk51vd69n54	7	21	,	,	PUNCT
zk51vd69n54	7	22	a	a	DET
zk51vd69n54	7	23	biclosed	biclosed	ADJ
zk51vd69n54	7	24	set	set	NOUN
zk51vd69n54	7	25	is	be	AUX
zk51vd69n54	7	26	an	an	DET
zk51vd69n54	7	27	inversion	inversion	NOUN
zk51vd69n54	7	28	set	set	VERB
zk51vd69n54	7	29	if	if	SCONJ
zk51vd69n54	7	30	and	and	CCONJ
zk51vd69n54	7	31	only	only	ADV
zk51vd69n54	7	32	if	if	SCONJ
zk51vd69n54	7	33	the	the	DET
zk51vd69n54	7	34	associated	associate	VERB
zk51vd69n54	7	35	twisted	twist	VERB
zk51vd69n54	7	36	weak	weak	ADJ
zk51vd69n54	7	37	order	order	NOUN
zk51vd69n54	7	38	on	on	ADP
zk51vd69n54	7	39	the	the	DET
zk51vd69n54	7	40	group	group	NOUN
zk51vd69n54	7	41	is	be	AUX
zk51vd69n54	7	42	a	a	DET
zk51vd69n54	7	43	meet	meet	NOUN
zk51vd69n54	7	44	semilattice	semilattice	NOUN
zk51vd69n54	7	45	.	.	PUNCT
zk51vd69n54	8	1	these	these	DET
zk51vd69n54	8	2	results	result	NOUN
zk51vd69n54	8	3	are	be	AUX
zk51vd69n54	8	4	analogous	analogous	ADJ
zk51vd69n54	8	5	to	to	ADP
zk51vd69n54	8	6	the	the	DET
zk51vd69n54	8	7	fact	fact	NOUN
zk51vd69n54	8	8	that	that	SCONJ
zk51vd69n54	8	9	the	the	DET
zk51vd69n54	8	10	weak	weak	ADJ
zk51vd69n54	8	11	order	order	NOUN
zk51vd69n54	8	12	of	of	ADP
zk51vd69n54	8	13	a	a	DET
zk51vd69n54	8	14	simplicial	simplicial	ADJ
zk51vd69n54	8	15	base	base	NOUN
zk51vd69n54	8	16	chamber	chamber	NOUN
zk51vd69n54	8	17	of	of	ADP
zk51vd69n54	8	18	a	a	DET
zk51vd69n54	8	19	finite	finite	ADJ
zk51vd69n54	8	20	simple	simple	ADJ
zk51vd69n54	8	21	oriented	orient	VERB
zk51vd69n54	8	22	matroid	matroid	NOUN
zk51vd69n54	8	23	is	be	AUX
zk51vd69n54	8	24	a	a	DET
zk51vd69n54	8	25	complete	complete	ADJ
zk51vd69n54	8	26	lattice	lattice	NOUN
zk51vd69n54	8	27	(	(	PUNCT
zk51vd69n54	8	28	such	such	ADJ
zk51vd69n54	8	29	order	order	NOUN
zk51vd69n54	8	30	is	be	AUX
zk51vd69n54	8	31	defined	define	VERB
zk51vd69n54	8	32	on	on	ADP
zk51vd69n54	8	33	the	the	DET
zk51vd69n54	8	34	family	family	NOUN
zk51vd69n54	8	35	of	of	ADP
zk51vd69n54	8	36	biconvex	biconvex	PROPN
zk51vd69n54	8	37	sets	set	NOUN
zk51vd69n54	8	38	of	of	ADP
zk51vd69n54	8	39	a	a	DET
zk51vd69n54	8	40	given	give	VERB
zk51vd69n54	8	41	hemispace	hemispace	NOUN
zk51vd69n54	8	42	under	under	ADP
zk51vd69n54	8	43	inclusion).finally	inclusion).finally	ADV
zk51vd69n54	8	44	,	,	PUNCT
zk51vd69n54	8	45	we	we	PRON
zk51vd69n54	8	46	treat	treat	VERB
zk51vd69n54	8	47	the	the	DET
zk51vd69n54	8	48	root	root	NOUN
zk51vd69n54	8	49	systems	system	NOUN
zk51vd69n54	8	50	of	of	ADP
zk51vd69n54	8	51	an	an	DET
zk51vd69n54	8	52	affine	affine	ADJ
zk51vd69n54	8	53	weyl	weyl	NOUN
zk51vd69n54	8	54	group	group	NOUN
zk51vd69n54	8	55	as	as	ADP
zk51vd69n54	8	56	an	an	DET
zk51vd69n54	8	57	infinite	infinite	ADJ
zk51vd69n54	8	58	oriented	orient	VERB
zk51vd69n54	8	59	matroid	matroid	NOUN
zk51vd69n54	8	60	in	in	ADP
zk51vd69n54	8	61	the	the	DET
zk51vd69n54	8	62	sense	sense	NOUN
zk51vd69n54	8	63	of	of	ADP
zk51vd69n54	8	64	buchi	buchi	NOUN
zk51vd69n54	8	65	and	and	CCONJ
zk51vd69n54	8	66	fenton	fenton	PROPN
zk51vd69n54	8	67	.	.	PUNCT
zk51vd69n54	9	1	we	we	PRON
zk51vd69n54	9	2	compute	compute	VERB
zk51vd69n54	9	3	all	all	PRON
zk51vd69n54	9	4	of	of	ADP
zk51vd69n54	9	5	their	their	PRON
zk51vd69n54	9	6	hemispaces	hemispace	NOUN
zk51vd69n54	9	7	,	,	PUNCT
zk51vd69n54	9	8	covectors	covector	NOUN
zk51vd69n54	9	9	and	and	CCONJ
zk51vd69n54	9	10	the	the	DET
zk51vd69n54	9	11	stabilizers	stabilizer	NOUN
zk51vd69n54	9	12	of	of	ADP
zk51vd69n54	9	13	the	the	DET
zk51vd69n54	9	14	covectors	covector	NOUN
zk51vd69n54	9	15	.	.	PUNCT
zk51vd69n54	10	1	also	also	ADV
zk51vd69n54	10	2	we	we	PRON
zk51vd69n54	10	3	describe	describe	VERB
zk51vd69n54	10	4	a	a	DET
zk51vd69n54	10	5	complete	complete	ADJ
zk51vd69n54	10	6	rootoid	rootoid	NOUN
zk51vd69n54	10	7	structure	structure	NOUN
zk51vd69n54	10	8	from	from	ADP
zk51vd69n54	10	9	locally	locally	ADV
zk51vd69n54	10	10	finite	finite	NOUN
zk51vd69n54	10	11	coxeter	coxeter	NOUN
zk51vd69n54	10	12	groups	group	NOUN
zk51vd69n54	10	13	which	which	PRON
zk51vd69n54	10	14	is	be	AUX
zk51vd69n54	10	15	analogous	analogous	ADJ
zk51vd69n54	10	16	to	to	ADP
zk51vd69n54	10	17	the	the	DET
zk51vd69n54	10	18	structure	structure	NOUN
zk51vd69n54	10	19	of	of	ADP
zk51vd69n54	10	20	a	a	DET
zk51vd69n54	10	21	simplicial	simplicial	ADJ
zk51vd69n54	10	22	oriented	orient	VERB
zk51vd69n54	10	23	geometry	geometry	NOUN
zk51vd69n54	10	24	.	.	PUNCT